diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index bbdcd183f65e1..7ff39525bf80d 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -652,7 +652,7 @@ Strings
 ^^^^^^^
 - Bug in :meth:`Series.to_string`, :meth:`DataFrame.to_string`, and :meth:`DataFrame.to_latex` adding a leading space when ``index=False`` (:issue:`24980`)
 - Bug in :func:`to_numeric` raising a ``TypeError`` when attempting to convert a string dtype Series containing only numeric strings and ``NA`` (:issue:`37262`)
--
+- Bug in :meth:`astype` raising ``ValueError`` when attempting to convert ``string`` dtype to ``timedelta64`` (:issue:`38509`)
 
 Interval
 ^^^^^^^^
diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index cc2013deb5252..4ca8f0e0c879b 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -21,6 +21,7 @@
 from pandas.core.arrays import FloatingArray, IntegerArray, PandasArray
 from pandas.core.arrays.floating import FloatingDtype
 from pandas.core.arrays.integer import _IntegerDtype
+from pandas.core.arrays.timedeltas import sequence_to_td64ns
 from pandas.core.construction import extract_array
 from pandas.core.indexers import check_array_indexer
 from pandas.core.missing import isna
@@ -308,6 +309,13 @@ def astype(self, dtype, copy=True):
             values = arr.astype(dtype)
             values[mask] = np.nan
             return values
+        elif np.issubdtype(dtype, np.timedelta64):
+            # GH 38509: handle conversion to timedelta64
+            arr = self.copy()
+            mask = self.isna()
+            arr[mask] = "NaT"
+            values, _ = sequence_to_td64ns(arr)
+            return values
 
         return super().astype(dtype, copy)
 
diff --git a/pandas/tests/arrays/string_/test_string.py b/pandas/tests/arrays/string_/test_string.py
index 5365929213503..a3b3dec7cda0d 100644
--- a/pandas/tests/arrays/string_/test_string.py
+++ b/pandas/tests/arrays/string_/test_string.py
@@ -5,7 +5,11 @@
 
 import pandas.util._test_decorators as td
 
-from pandas.core.dtypes.common import is_dtype_equal
+from pandas.core.dtypes.common import (
+    is_datetime64_dtype,
+    is_dtype_equal,
+    is_timedelta64_dtype,
+)
 
 import pandas as pd
 import pandas._testing as tm
@@ -123,24 +127,31 @@ def test_string_methods(input, method, dtype, request):
     tm.assert_series_equal(result.astype(object), expected)
 
 
-def test_astype_roundtrip(dtype, request):
+@pytest.mark.parametrize(
+    "input",
+    [
+        pd.date_range("2000", periods=12),
+        pd.timedelta_range("1 D", periods=3),
+    ],
+)
+def test_astype_roundtrip(input, dtype, request):
+    # GH 38509 (timedelta)
     if dtype == "arrow_string":
-        reason = "ValueError: Could not convert object to NumPy datetime"
-        mark = pytest.mark.xfail(reason=reason, raises=ValueError)
-        request.node.add_marker(mark)
-    else:
-        mark = pytest.mark.xfail(
-            reason="GH#36153 casting from StringArray to dt64 fails", raises=ValueError
-        )
+        if is_datetime64_dtype(input):
+            typename = "datetime"
+        elif is_timedelta64_dtype(input):
+            typename = "timedelta"
+        reason = f"ValueError: Could not convert object to NumPy {typename}"
+        mark = pytest.mark.xfail(reason=reason)
         request.node.add_marker(mark)
 
-    ser = pd.Series(pd.date_range("2000", periods=12))
+    ser = pd.Series(input)
     ser[0] = None
 
     casted = ser.astype(dtype)
     assert is_dtype_equal(casted.dtype, dtype)
 
-    result = casted.astype("datetime64[ns]")
+    result = casted.astype(ser.dtype)
     tm.assert_series_equal(result, ser)