diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 766c418741ada..ffd20df85ed1f 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -580,6 +580,7 @@ Conversion
 ^^^^^^^^^^
 
 - Bug in :meth:`DataFrame.to_dict` with ``orient='records'`` now returns python native datetime objects for datetimelike columns (:issue:`21256`)
+- Bug in :meth:`Series.astype` conversion from ``string`` to ``float`` raised in presence of ``pd.NA`` values (:issue:`37626`)
 -
 
 Strings
diff --git a/pandas/conftest.py b/pandas/conftest.py
index 77e9af67590a6..a2c137a1e1aed 100644
--- a/pandas/conftest.py
+++ b/pandas/conftest.py
@@ -286,7 +286,6 @@ def unique_nulls_fixture(request):
 # Generate cartesian product of unique_nulls_fixture:
 unique_nulls_fixture2 = unique_nulls_fixture
 
-
 # ----------------------------------------------------------------
 # Classes
 # ----------------------------------------------------------------
@@ -1069,6 +1068,20 @@ def float_ea_dtype(request):
     return request.param
 
 
+@pytest.fixture(params=tm.FLOAT_DTYPES + tm.FLOAT_EA_DTYPES)
+def any_float_allowed_nullable_dtype(request):
+    """
+    Parameterized fixture for float dtypes.
+
+    * float
+    * 'float32'
+    * 'float64'
+    * 'Float32'
+    * 'Float64'
+    """
+    return request.param
+
+
 @pytest.fixture(params=tm.COMPLEX_DTYPES)
 def complex_dtype(request):
     """
diff --git a/pandas/core/arrays/string_.py b/pandas/core/arrays/string_.py
index 3b297e7c2b13b..e0bb788d665eb 100644
--- a/pandas/core/arrays/string_.py
+++ b/pandas/core/arrays/string_.py
@@ -18,7 +18,8 @@
 
 from pandas.core import ops
 from pandas.core.array_algos import masked_reductions
-from pandas.core.arrays import IntegerArray, PandasArray
+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.construction import extract_array
 from pandas.core.indexers import check_array_indexer
@@ -298,6 +299,19 @@ def astype(self, dtype, copy=True):
             arr[mask] = 0
             values = arr.astype(dtype.numpy_dtype)
             return IntegerArray(values, mask, copy=False)
+        elif isinstance(dtype, FloatingDtype):
+            arr = self.copy()
+            mask = self.isna()
+            arr[mask] = "0"
+            values = arr.astype(dtype.numpy_dtype)
+            return FloatingArray(values, mask, copy=False)
+        elif np.issubdtype(dtype, np.floating):
+            arr = self._ndarray.copy()
+            mask = self.isna()
+            arr[mask] = 0
+            values = arr.astype(dtype)
+            values[mask] = np.nan
+            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 07e9484994c26..b629e2fca2feb 100644
--- a/pandas/tests/arrays/string_/test_string.py
+++ b/pandas/tests/arrays/string_/test_string.py
@@ -366,6 +366,15 @@ def test_astype_int(dtype, request):
     tm.assert_extension_array_equal(result, expected)
 
 
+def test_astype_float(any_float_allowed_nullable_dtype):
+    # Don't compare arrays (37974)
+    ser = pd.Series(["1.1", pd.NA, "3.3"], dtype="string")
+
+    result = ser.astype(any_float_allowed_nullable_dtype)
+    expected = pd.Series([1.1, np.nan, 3.3], dtype=any_float_allowed_nullable_dtype)
+    tm.assert_series_equal(result, expected)
+
+
 @pytest.mark.parametrize("skipna", [True, False])
 @pytest.mark.xfail(reason="Not implemented StringArray.sum")
 def test_reduce(skipna, dtype):