diff --git a/docs/api/utilities.rst b/docs/api/utilities.rst
index 9b909431..f404113f 100644
--- a/docs/api/utilities.rst
+++ b/docs/api/utilities.rst
@@ -99,6 +99,7 @@ Tree
     tree_get_all_with_path
     tree_l1_norm
     tree_l2_norm
+    tree_linf_norm
     tree_map_params
     tree_max
     tree_mul
@@ -153,6 +154,10 @@ Tree l2 norm
 ~~~~~~~~~~~~
 .. autofunction:: tree_l2_norm
 
+Tree l-infinity norm
+~~~~~~~~~~~~~~~~~~~~
+.. autofunction:: tree_linf_norm
+
 Tree map parameters
 ~~~~~~~~~~~~~~~~~~~
 .. autofunction:: tree_map_params
diff --git a/optax/tree_utils/__init__.py b/optax/tree_utils/__init__.py
index 9675ad02..0887a9ab 100644
--- a/optax/tree_utils/__init__.py
+++ b/optax/tree_utils/__init__.py
@@ -32,6 +32,7 @@
 from optax.tree_utils._tree_math import tree_full_like
 from optax.tree_utils._tree_math import tree_l1_norm
 from optax.tree_utils._tree_math import tree_l2_norm
+from optax.tree_utils._tree_math import tree_linf_norm
 from optax.tree_utils._tree_math import tree_max
 from optax.tree_utils._tree_math import tree_mul
 from optax.tree_utils._tree_math import tree_ones_like
diff --git a/optax/tree_utils/_tree_math.py b/optax/tree_utils/_tree_math.py
index 3d52c23c..ca969141 100644
--- a/optax/tree_utils/_tree_math.py
+++ b/optax/tree_utils/_tree_math.py
@@ -217,6 +217,19 @@ def tree_l1_norm(tree: Any) -> chex.Numeric:
   return tree_sum(abs_tree)
 
 
+def tree_linf_norm(tree: Any) -> chex.Numeric:
+  """Compute the l-infinity norm of a pytree.
+
+  Args:
+    tree: pytree.
+
+  Returns:
+    a scalar value.
+  """
+  abs_tree = jax.tree.map(jnp.abs, tree)
+  return tree_max(abs_tree)
+
+
 def tree_zeros_like(
     tree: Any,
     dtype: Optional[jax.typing.DTypeLike] = None,
diff --git a/optax/tree_utils/_tree_math_test.py b/optax/tree_utils/_tree_math_test.py
index 054f239d..3feb4e13 100644
--- a/optax/tree_utils/_tree_math_test.py
+++ b/optax/tree_utils/_tree_math_test.py
@@ -163,6 +163,16 @@ def test_tree_l1_norm(self, key):
     got = tu.tree_l1_norm(tree)
     np.testing.assert_allclose(expected, got, atol=1e-4)
 
+  @parameterized.parameters(
+      'tree_a', 'tree_a_dict', 'tree_b', 'array_a', 'array_b', 'tree_b_dict'
+  )
+  def test_tree_linf_norm(self, key):
+    tree = self.data[key]
+    values, _ = flatten_util.ravel_pytree(tree)
+    expected = jnp.max(jnp.abs(values))
+    got = tu.tree_linf_norm(tree)
+    np.testing.assert_allclose(expected, got, atol=1e-4)
+
   def test_tree_zeros_like(self):
     expected = jnp.zeros_like(self.array_a)
     got = tu.tree_zeros_like(self.array_a)