diff --git a/src/compiler/parser.ts b/src/compiler/parser.ts
index c5cbb950f69d7..8f7ea52ebe94b 100644
--- a/src/compiler/parser.ts
+++ b/src/compiler/parser.ts
@@ -2701,19 +2701,10 @@ namespace ts {
             return finishNode(factory.createThisTypeNode(), pos);
         }
 
-        function parseJSDocAllType(postFixEquals: boolean): JSDocAllType | JSDocOptionalType {
+        function parseJSDocAllType(): JSDocAllType | JSDocOptionalType {
             const pos = getNodePos();
             nextToken();
-
-            const node = factory.createJSDocAllType();
-            if (postFixEquals) {
-                // Trim the trailing `=` from the `*=` token
-                const end = Math.max(getNodePos() - 1, pos);
-                return finishNode(factory.createJSDocOptionalType(finishNode(node, pos, end)), pos);
-            }
-            else {
-                return finishNode(node, pos);
-            }
+            return finishNode(factory.createJSDocAllType(), pos);
         }
 
         function parseJSDocNonNullableType(): TypeNode {
@@ -3396,12 +3387,14 @@ namespace ts {
                 case SyntaxKind.ObjectKeyword:
                     // If these are followed by a dot, then parse these out as a dotted type reference instead.
                     return tryParse(parseKeywordAndNoDot) || parseTypeReference();
-                case SyntaxKind.AsteriskToken:
-                    return parseJSDocAllType(/*postfixEquals*/ false);
                 case SyntaxKind.AsteriskEqualsToken:
-                    return parseJSDocAllType(/*postfixEquals*/ true);
+                    // If there is '*=', treat it as * followed by postfix =
+                    scanner.reScanAsteriskEqualsToken();
+                    // falls through
+                case SyntaxKind.AsteriskToken:
+                    return parseJSDocAllType();
                 case SyntaxKind.QuestionQuestionToken:
-                    // If there is '??', consider that is prefix '?' in JSDoc type.
+                    // If there is '??', treat it as prefix-'?' in JSDoc type.
                     scanner.reScanQuestionToken();
                     // falls through
                 case SyntaxKind.QuestionToken:
diff --git a/src/compiler/scanner.ts b/src/compiler/scanner.ts
index b58ae9aee773c..0a4e5126987eb 100644
--- a/src/compiler/scanner.ts
+++ b/src/compiler/scanner.ts
@@ -34,6 +34,7 @@ namespace ts {
         getTokenFlags(): TokenFlags;
         reScanGreaterToken(): SyntaxKind;
         reScanSlashToken(): SyntaxKind;
+        reScanAsteriskEqualsToken(): SyntaxKind;
         reScanTemplateToken(isTaggedTemplate: boolean): SyntaxKind;
         reScanTemplateHeadOrNoSubstitutionTemplate(): SyntaxKind;
         scanJsxIdentifier(): SyntaxKind;
@@ -954,6 +955,7 @@ namespace ts {
             getNumericLiteralFlags: () => tokenFlags & TokenFlags.NumericLiteralFlags,
             getTokenFlags: () => tokenFlags,
             reScanGreaterToken,
+            reScanAsteriskEqualsToken,
             reScanSlashToken,
             reScanTemplateToken,
             reScanTemplateHeadOrNoSubstitutionTemplate,
@@ -2086,6 +2088,12 @@ namespace ts {
             return token;
         }
 
+        function reScanAsteriskEqualsToken(): SyntaxKind {
+            Debug.assert(token === SyntaxKind.AsteriskEqualsToken, "'reScanAsteriskEqualsToken' should only be called on a '*='");
+            pos = tokenPos + 1;
+            return token = SyntaxKind.EqualsToken;
+        }
+
         function reScanSlashToken(): SyntaxKind {
             if (token === SyntaxKind.SlashToken || token === SyntaxKind.SlashEqualsToken) {
                 let p = tokenPos + 1;
diff --git a/tests/baselines/reference/api/tsserverlibrary.d.ts b/tests/baselines/reference/api/tsserverlibrary.d.ts
index 360aa0650053d..83b03093da4b0 100644
--- a/tests/baselines/reference/api/tsserverlibrary.d.ts
+++ b/tests/baselines/reference/api/tsserverlibrary.d.ts
@@ -3902,6 +3902,7 @@ declare namespace ts {
         isUnterminated(): boolean;
         reScanGreaterToken(): SyntaxKind;
         reScanSlashToken(): SyntaxKind;
+        reScanAsteriskEqualsToken(): SyntaxKind;
         reScanTemplateToken(isTaggedTemplate: boolean): SyntaxKind;
         reScanTemplateHeadOrNoSubstitutionTemplate(): SyntaxKind;
         scanJsxIdentifier(): SyntaxKind;
diff --git a/tests/baselines/reference/api/typescript.d.ts b/tests/baselines/reference/api/typescript.d.ts
index d30b0b8f7ac84..e85e4a8bf70b2 100644
--- a/tests/baselines/reference/api/typescript.d.ts
+++ b/tests/baselines/reference/api/typescript.d.ts
@@ -3902,6 +3902,7 @@ declare namespace ts {
         isUnterminated(): boolean;
         reScanGreaterToken(): SyntaxKind;
         reScanSlashToken(): SyntaxKind;
+        reScanAsteriskEqualsToken(): SyntaxKind;
         reScanTemplateToken(isTaggedTemplate: boolean): SyntaxKind;
         reScanTemplateHeadOrNoSubstitutionTemplate(): SyntaxKind;
         scanJsxIdentifier(): SyntaxKind;
diff --git a/tests/baselines/reference/jsdocParseStarEquals.symbols b/tests/baselines/reference/jsdocParseStarEquals.symbols
index a882cf23eb21c..795d97f20b853 100644
--- a/tests/baselines/reference/jsdocParseStarEquals.symbols
+++ b/tests/baselines/reference/jsdocParseStarEquals.symbols
@@ -12,3 +12,10 @@ function f(...args) {
 var x;
 >x : Symbol(x, Decl(a.js, 7, 3))
 
+
+/** @param {function():*=} f */
+function cbf(f) {
+>cbf : Symbol(cbf, Decl(a.js, 7, 6))
+>f : Symbol(f, Decl(a.js, 11, 13))
+}
+
diff --git a/tests/baselines/reference/jsdocParseStarEquals.types b/tests/baselines/reference/jsdocParseStarEquals.types
index 1142fb05daea3..174e543dd7d92 100644
--- a/tests/baselines/reference/jsdocParseStarEquals.types
+++ b/tests/baselines/reference/jsdocParseStarEquals.types
@@ -2,8 +2,8 @@
 /** @param {...*=} args
     @return {*=} */
 function f(...args) {
->f : (...args: (any | undefined)[]) => any | undefined
->args : any[]
+>f : (...args?: any[] | undefined) => any | undefined
+>args : any
 
     return null
 >null : null
@@ -13,3 +13,10 @@ function f(...args) {
 var x;
 >x : any
 
+
+/** @param {function():*=} f */
+function cbf(f) {
+>cbf : (f?: (() => any) | undefined) => void
+>f : (() => any) | undefined
+}
+
diff --git a/tests/cases/conformance/jsdoc/jsdocParseStarEquals.ts b/tests/cases/conformance/jsdoc/jsdocParseStarEquals.ts
index e5f07bb3d2f6d..ef93965e0fc87 100644
--- a/tests/cases/conformance/jsdoc/jsdocParseStarEquals.ts
+++ b/tests/cases/conformance/jsdoc/jsdocParseStarEquals.ts
@@ -12,3 +12,8 @@ function f(...args) {
 
 /** @type *= */
 var x;
+
+
+/** @param {function():*=} f */
+function cbf(f) {
+}