diff --git a/doc/source/whatsnew/v0.22.0.txt b/doc/source/whatsnew/v0.22.0.txt
index 0579a80aad28e..1a19033ac61ee 100644
--- a/doc/source/whatsnew/v0.22.0.txt
+++ b/doc/source/whatsnew/v0.22.0.txt
@@ -277,6 +277,7 @@ Conversion
 - Fixed a bug where ``FY5253`` date offsets could incorrectly raise an ``AssertionError`` in arithmetic operatons (:issue:`14774`)
 - Bug in :meth:`Index.astype` with a categorical dtype where the resultant index is not converted to a :class:`CategoricalIndex` for all types of index (:issue:`18630`)
 - Bug in :meth:`Series.astype` and ``Categorical.astype()`` where an existing categorical data does not get updated (:issue:`10696`, :issue:`18593`)
+- Bug in :class:`Series` constructor with an int or float list where specifying ``dtype=str``, ``dtype='str'`` or ``dtype='U'`` failed to convert the data elements to strings (:issue:`16605`)
 
 
 Indexing
diff --git a/pandas/core/series.py b/pandas/core/series.py
index a3e7be1bfb35a..a1d296deae319 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -3277,6 +3277,11 @@ def _try_cast(arr, take_fast_path):
     # This is to prevent mixed-type Series getting all casted to
     # NumPy string type, e.g. NaN --> '-1#IND'.
     if issubclass(subarr.dtype.type, compat.string_types):
+        # GH 16605
+        # If not empty convert the data to dtype
+        if not isna(data).all():
+            data = np.array(data, dtype=dtype, copy=False)
+
         subarr = np.array(data, dtype=object, copy=copy)
 
     return subarr
diff --git a/pandas/tests/frame/test_dtypes.py b/pandas/tests/frame/test_dtypes.py
index 610b9f7bdbf6c..21c028e634bc0 100644
--- a/pandas/tests/frame/test_dtypes.py
+++ b/pandas/tests/frame/test_dtypes.py
@@ -676,6 +676,25 @@ def test_arg_for_errors_in_astype(self):
 
         df.astype(np.int8, errors='ignore')
 
+    @pytest.mark.parametrize('input_vals', [
+        ([1, 2]),
+        ([1.0, 2.0, np.nan]),
+        (['1', '2']),
+        (list(pd.date_range('1/1/2011', periods=2, freq='H'))),
+        (list(pd.date_range('1/1/2011', periods=2, freq='H',
+                            tz='US/Eastern'))),
+        ([pd.Interval(left=0, right=5)]),
+    ])
+    def test_constructor_list_str(self, input_vals):
+        # GH 16605
+        # Ensure that data elements are converted to strings when
+        # dtype is str, 'str', or 'U'
+
+        for dtype in ['str', str, 'U']:
+            result = DataFrame({'A': input_vals}, dtype=dtype)
+            expected = DataFrame({'A': input_vals}).astype({'A': dtype})
+            assert_frame_equal(result, expected)
+
 
 class TestDataFrameDatetimeWithTZ(TestData):
 
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index f9842514ed5e5..08416fe34efcc 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -142,6 +142,25 @@ def test_constructor_list_like(self):
             result = Series(obj, index=[0, 1, 2])
             assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize('input_vals', [
+        ([1, 2]),
+        ([1.0, 2.0, np.nan]),
+        (['1', '2']),
+        (list(pd.date_range('1/1/2011', periods=2, freq='H'))),
+        (list(pd.date_range('1/1/2011', periods=2, freq='H',
+                            tz='US/Eastern'))),
+        ([pd.Interval(left=0, right=5)]),
+    ])
+    def test_constructor_list_str(self, input_vals):
+        # GH 16605
+        # Ensure that data elements from a list are converted to strings
+        # when dtype is str, 'str', or 'U'
+
+        for dtype in ['str', str, 'U']:
+            result = Series(input_vals, dtype=dtype)
+            expected = Series(input_vals).astype(dtype)
+            assert_series_equal(result, expected)
+
     def test_constructor_generator(self):
         gen = (i for i in range(10))