diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index f313b49cd198d..7a90d96926475 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -802,6 +802,7 @@ Performance improvements
 - Performance improvement in datetime arrays string formatting when one of the default strftime formats ``"%Y-%m-%d %H:%M:%S"`` or ``"%Y-%m-%d %H:%M:%S.%f"`` is used. (:issue:`44764`)
 - Performance improvement in :meth:`Series.to_sql` and :meth:`DataFrame.to_sql` (:class:`SQLiteTable`) when processing time arrays. (:issue:`44764`)
 - Performance improvements to :func:`read_sas` (:issue:`47403`, :issue:`47404`, :issue:`47405`)
+- Performance improvement in ``argmax`` and ``argmin`` for :class:`arrays.SparseArray` (:issue:`34197`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/arrays/sparse/array.py b/pandas/core/arrays/sparse/array.py
index 5653d87a4570b..bf65da0412642 100644
--- a/pandas/core/arrays/sparse/array.py
+++ b/pandas/core/arrays/sparse/array.py
@@ -42,7 +42,10 @@
 from pandas.compat.numpy import function as nv
 from pandas.errors import PerformanceWarning
 from pandas.util._exceptions import find_stack_level
-from pandas.util._validators import validate_insert_loc
+from pandas.util._validators import (
+    validate_bool_kwarg,
+    validate_insert_loc,
+)
 
 from pandas.core.dtypes.astype import astype_nansafe
 from pandas.core.dtypes.cast import (
@@ -1636,6 +1639,45 @@ def _min_max(self, kind: Literal["min", "max"], skipna: bool) -> Scalar:
         else:
             return na_value_for_dtype(self.dtype.subtype, compat=False)
 
+    def _argmin_argmax(self, kind: Literal["argmin", "argmax"]) -> int:
+
+        values = self._sparse_values
+        index = self._sparse_index.indices
+        mask = np.asarray(isna(values))
+        func = np.argmax if kind == "argmax" else np.argmin
+
+        idx = np.arange(values.shape[0])
+        non_nans = values[~mask]
+        non_nan_idx = idx[~mask]
+
+        _candidate = non_nan_idx[func(non_nans)]
+        candidate = index[_candidate]
+
+        if isna(self.fill_value):
+            return candidate
+        if kind == "argmin" and self[candidate] < self.fill_value:
+            return candidate
+        if kind == "argmax" and self[candidate] > self.fill_value:
+            return candidate
+        _loc = self._first_fill_value_loc()
+        if _loc == -1:
+            # fill_value doesn't exist
+            return candidate
+        else:
+            return _loc
+
+    def argmax(self, skipna: bool = True) -> int:
+        validate_bool_kwarg(skipna, "skipna")
+        if not skipna and self._hasna:
+            raise NotImplementedError
+        return self._argmin_argmax("argmax")
+
+    def argmin(self, skipna: bool = True) -> int:
+        validate_bool_kwarg(skipna, "skipna")
+        if not skipna and self._hasna:
+            raise NotImplementedError
+        return self._argmin_argmax("argmin")
+
     # ------------------------------------------------------------------------
     # Ufuncs
     # ------------------------------------------------------------------------
diff --git a/pandas/tests/arrays/sparse/test_reductions.py b/pandas/tests/arrays/sparse/test_reductions.py
index a33a282bb4869..2dd80c52f1419 100644
--- a/pandas/tests/arrays/sparse/test_reductions.py
+++ b/pandas/tests/arrays/sparse/test_reductions.py
@@ -268,3 +268,41 @@ def test_na_value_if_no_valid_values(self, func, data, dtype, expected):
             assert result is NaT or np.isnat(result)
         else:
             assert np.isnan(result)
+
+
+class TestArgmaxArgmin:
+    @pytest.mark.parametrize(
+        "arr,argmax_expected,argmin_expected",
+        [
+            (SparseArray([1, 2, 0, 1, 2]), 1, 2),
+            (SparseArray([-1, -2, 0, -1, -2]), 2, 1),
+            (SparseArray([np.nan, 1, 0, 0, np.nan, -1]), 1, 5),
+            (SparseArray([np.nan, 1, 0, 0, np.nan, 2]), 5, 2),
+            (SparseArray([np.nan, 1, 0, 0, np.nan, 2], fill_value=-1), 5, 2),
+            (SparseArray([np.nan, 1, 0, 0, np.nan, 2], fill_value=0), 5, 2),
+            (SparseArray([np.nan, 1, 0, 0, np.nan, 2], fill_value=1), 5, 2),
+            (SparseArray([np.nan, 1, 0, 0, np.nan, 2], fill_value=2), 5, 2),
+            (SparseArray([np.nan, 1, 0, 0, np.nan, 2], fill_value=3), 5, 2),
+            (SparseArray([0] * 10 + [-1], fill_value=0), 0, 10),
+            (SparseArray([0] * 10 + [-1], fill_value=-1), 0, 10),
+            (SparseArray([0] * 10 + [-1], fill_value=1), 0, 10),
+            (SparseArray([-1] + [0] * 10, fill_value=0), 1, 0),
+            (SparseArray([1] + [0] * 10, fill_value=0), 0, 1),
+            (SparseArray([-1] + [0] * 10, fill_value=-1), 1, 0),
+            (SparseArray([1] + [0] * 10, fill_value=1), 0, 1),
+        ],
+    )
+    def test_argmax_argmin(self, arr, argmax_expected, argmin_expected):
+        argmax_result = arr.argmax()
+        argmin_result = arr.argmin()
+        assert argmax_result == argmax_expected
+        assert argmin_result == argmin_expected
+
+    @pytest.mark.parametrize(
+        "arr,method",
+        [(SparseArray([]), "argmax"), (SparseArray([]), "argmin")],
+    )
+    def test_empty_array(self, arr, method):
+        msg = f"attempt to get {method} of an empty sequence"
+        with pytest.raises(ValueError, match=msg):
+            arr.argmax() if method == "argmax" else arr.argmin()