diff --git a/doc/source/whatsnew/v1.1.2.rst b/doc/source/whatsnew/v1.1.2.rst
index dea3cb6f567ac..1c3258db28698 100644
--- a/doc/source/whatsnew/v1.1.2.rst
+++ b/doc/source/whatsnew/v1.1.2.rst
@@ -33,6 +33,7 @@ Bug fixes
 - Bug in :meth:`DataFrame.eval` with ``object`` dtype column binary operations (:issue:`35794`)
 - Bug in :class:`Series` constructor raising a ``TypeError`` when constructing sparse datetime64 dtypes (:issue:`35762`)
 - Bug in :meth:`DataFrame.apply` with ``result_type="reduce"`` returning with incorrect index (:issue:`35683`)
+- Bug in :meth:`Series.astype` and :meth:`DataFrame.astype` not respecting the ``errors`` argument when set to ``"ignore"`` for extension dtypes (:issue:`35471`)
 - Bug in :meth:`DateTimeIndex.format` and :meth:`PeriodIndex.format` with ``name=True`` setting the first item to ``"None"`` where it should be ``""`` (:issue:`35712`)
 - Bug in :meth:`Float64Index.__contains__` incorrectly raising ``TypeError`` instead of returning ``False`` (:issue:`35788`)
 - Bug in :class:`Series` constructor incorrectly raising a ``TypeError`` when passed an ordered set (:issue:`36044`)
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index f4f4a3666a84e..ea2b0c972d9aa 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -565,8 +565,13 @@ def astype(self, dtype, copy: bool = False, errors: str = "raise"):
 
         # force the copy here
         if self.is_extension:
-            # TODO: Should we try/except this astype?
-            values = self.values.astype(dtype)
+            try:
+                values = self.values.astype(dtype)
+            except (ValueError, TypeError):
+                if errors == "ignore":
+                    values = self.values
+                else:
+                    raise
         else:
             if issubclass(dtype.type, str):
 
diff --git a/pandas/tests/frame/methods/test_astype.py b/pandas/tests/frame/methods/test_astype.py
index b0fd0496ea81e..d3f256259b15f 100644
--- a/pandas/tests/frame/methods/test_astype.py
+++ b/pandas/tests/frame/methods/test_astype.py
@@ -8,6 +8,7 @@
     CategoricalDtype,
     DataFrame,
     DatetimeTZDtype,
+    Interval,
     IntervalDtype,
     NaT,
     Series,
@@ -565,3 +566,24 @@ def test_astype_empty_dtype_dict(self):
         result = df.astype(dict())
         tm.assert_frame_equal(result, df)
         assert result is not df
+
+    @pytest.mark.parametrize(
+        "df",
+        [
+            DataFrame(Series(["x", "y", "z"], dtype="string")),
+            DataFrame(Series(["x", "y", "z"], dtype="category")),
+            DataFrame(Series(3 * [Timestamp("2020-01-01", tz="UTC")])),
+            DataFrame(Series(3 * [Interval(0, 1)])),
+        ],
+    )
+    @pytest.mark.parametrize("errors", ["raise", "ignore"])
+    def test_astype_ignores_errors_for_extension_dtypes(self, df, errors):
+        # https://github.com/pandas-dev/pandas/issues/35471
+        if errors == "ignore":
+            expected = df
+            result = df.astype(float, errors=errors)
+            tm.assert_frame_equal(result, expected)
+        else:
+            msg = "(Cannot cast)|(could not convert)"
+            with pytest.raises((ValueError, TypeError), match=msg):
+                df.astype(float, errors=errors)
diff --git a/pandas/tests/series/methods/test_astype.py b/pandas/tests/series/methods/test_astype.py
index 9fdc4179de2e1..b9d90a9fc63dd 100644
--- a/pandas/tests/series/methods/test_astype.py
+++ b/pandas/tests/series/methods/test_astype.py
@@ -1,4 +1,6 @@
-from pandas import Series, date_range
+import pytest
+
+from pandas import Interval, Series, Timestamp, date_range
 import pandas._testing as tm
 
 
@@ -23,3 +25,24 @@ def test_astype_dt64tz_to_str(self):
             dtype=object,
         )
         tm.assert_series_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "values",
+        [
+            Series(["x", "y", "z"], dtype="string"),
+            Series(["x", "y", "z"], dtype="category"),
+            Series(3 * [Timestamp("2020-01-01", tz="UTC")]),
+            Series(3 * [Interval(0, 1)]),
+        ],
+    )
+    @pytest.mark.parametrize("errors", ["raise", "ignore"])
+    def test_astype_ignores_errors_for_extension_dtypes(self, values, errors):
+        # https://github.com/pandas-dev/pandas/issues/35471
+        if errors == "ignore":
+            expected = values
+            result = values.astype(float, errors="ignore")
+            tm.assert_series_equal(result, expected)
+        else:
+            msg = "(Cannot cast)|(could not convert)"
+            with pytest.raises((ValueError, TypeError), match=msg):
+                values.astype(float, errors=errors)