diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index b31f7c1166dc0..448779e4c3e0b 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -36,8 +36,10 @@ Bug fixes
 
 - Using ``pd.NA`` with :meth:`DataFrame.to_json` now correctly outputs a null value instead of an empty object (:issue:`31615`)
 
+
 **Experimental dtypes**
 
+- Fix bug in :meth:`DataFrame.convert_dtypes` for columns that were already using the ``"string"`` dtype (:issue:`31731`).
 - Fixed bug in setting values using a slice indexer with string dtype (:issue:`31772`)
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_libs/lib.pyx b/pandas/_libs/lib.pyx
index 9702eb4615909..d2f0b2ffbaeec 100644
--- a/pandas/_libs/lib.pyx
+++ b/pandas/_libs/lib.pyx
@@ -1005,7 +1005,7 @@ _TYPE_MAP = {
     'complex64': 'complex',
     'complex128': 'complex',
     'c': 'complex',
-    'string': 'bytes',
+    'string': 'string',
     'S': 'bytes',
     'U': 'string',
     'bool': 'boolean',
diff --git a/pandas/conftest.py b/pandas/conftest.py
index 7463b2b579c0c..821bec19d6115 100644
--- a/pandas/conftest.py
+++ b/pandas/conftest.py
@@ -744,6 +744,7 @@ def any_numpy_dtype(request):
 # categoricals are handled separately
 _any_skipna_inferred_dtype = [
     ("string", ["a", np.nan, "c"]),
+    ("string", ["a", pd.NA, "c"]),
     ("bytes", [b"a", np.nan, b"c"]),
     ("empty", [np.nan, np.nan, np.nan]),
     ("empty", []),
@@ -754,6 +755,7 @@ def any_numpy_dtype(request):
     ("mixed-integer-float", [1, np.nan, 2.0]),
     ("decimal", [Decimal(1), np.nan, Decimal(2)]),
     ("boolean", [True, np.nan, False]),
+    ("boolean", [True, pd.NA, False]),
     ("datetime64", [np.datetime64("2013-01-01"), np.nan, np.datetime64("2018-01-01")]),
     ("datetime", [pd.Timestamp("20130101"), np.nan, pd.Timestamp("20180101")]),
     ("date", [date(2013, 1, 1), np.nan, date(2018, 1, 1)]),
diff --git a/pandas/tests/dtypes/test_inference.py b/pandas/tests/dtypes/test_inference.py
index 48f9262ad3486..48ae1f67297af 100644
--- a/pandas/tests/dtypes/test_inference.py
+++ b/pandas/tests/dtypes/test_inference.py
@@ -1200,6 +1200,24 @@ def test_interval(self):
         inferred = lib.infer_dtype(pd.Series(idx), skipna=False)
         assert inferred == "interval"
 
+    @pytest.mark.parametrize("klass", [pd.array, pd.Series])
+    @pytest.mark.parametrize("skipna", [True, False])
+    @pytest.mark.parametrize("data", [["a", "b", "c"], ["a", "b", pd.NA]])
+    def test_string_dtype(self, data, skipna, klass):
+        # StringArray
+        val = klass(data, dtype="string")
+        inferred = lib.infer_dtype(val, skipna=skipna)
+        assert inferred == "string"
+
+    @pytest.mark.parametrize("klass", [pd.array, pd.Series])
+    @pytest.mark.parametrize("skipna", [True, False])
+    @pytest.mark.parametrize("data", [[True, False, True], [True, False, pd.NA]])
+    def test_boolean_dtype(self, data, skipna, klass):
+        # BooleanArray
+        val = klass(data, dtype="boolean")
+        inferred = lib.infer_dtype(val, skipna=skipna)
+        assert inferred == "boolean"
+
 
 class TestNumberScalar:
     def test_is_number(self):
diff --git a/pandas/tests/series/methods/test_convert_dtypes.py b/pandas/tests/series/methods/test_convert_dtypes.py
index 923b5a94c5f41..a6b5fed40a9d7 100644
--- a/pandas/tests/series/methods/test_convert_dtypes.py
+++ b/pandas/tests/series/methods/test_convert_dtypes.py
@@ -246,3 +246,12 @@ def test_convert_dtypes(self, data, maindtype, params, answerdict):
 
         # Make sure original not changed
         tm.assert_series_equal(series, copy)
+
+    def test_convert_string_dtype(self):
+        # https://github.com/pandas-dev/pandas/issues/31731 -> converting columns
+        # that are already string dtype
+        df = pd.DataFrame(
+            {"A": ["a", "b", pd.NA], "B": ["ä", "ö", "ü"]}, dtype="string"
+        )
+        result = df.convert_dtypes()
+        tm.assert_frame_equal(df, result)
diff --git a/pandas/tests/test_strings.py b/pandas/tests/test_strings.py
index 62d26dacde67b..1338d801e39f4 100644
--- a/pandas/tests/test_strings.py
+++ b/pandas/tests/test_strings.py
@@ -7,6 +7,7 @@
 
 from pandas._libs import lib
 
+import pandas as pd
 from pandas import DataFrame, Index, MultiIndex, Series, concat, isna, notna
 import pandas._testing as tm
 import pandas.core.strings as strings
@@ -207,6 +208,9 @@ def test_api_per_dtype(self, index_or_series, dtype, any_skipna_inferred_dtype):
         box = index_or_series
         inferred_dtype, values = any_skipna_inferred_dtype
 
+        if dtype == "category" and len(values) and values[1] is pd.NA:
+            pytest.xfail(reason="Categorical does not yet support pd.NA")
+
         t = box(values, dtype=dtype)  # explicit dtype to avoid casting
 
         # TODO: get rid of these xfails