diff --git a/docs/api/projections.rst b/docs/api/projections.rst
index 243f848b..556377c2 100644
--- a/docs/api/projections.rst
+++ b/docs/api/projections.rst
@@ -37,6 +37,7 @@ Available projections
     projection_l1_sphere
     projection_l2_ball
     projection_l2_sphere
+    projection_linf_ball
     projection_non_negative
     projection_simplex
 
@@ -64,6 +65,10 @@ Projection onto the L2 sphere
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 .. autofunction:: projection_l2_sphere
 
+Projection onto the L-infinity ball
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+.. autofunction:: projection_linf_ball
+
 Projection onto the non-negative orthant
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 .. autofunction:: projection_non_negative
diff --git a/optax/projections/__init__.py b/optax/projections/__init__.py
index 6e6e45e5..19171ce6 100644
--- a/optax/projections/__init__.py
+++ b/optax/projections/__init__.py
@@ -21,5 +21,6 @@
 from optax.projections._projections import projection_l1_sphere
 from optax.projections._projections import projection_l2_ball
 from optax.projections._projections import projection_l2_sphere
+from optax.projections._projections import projection_linf_ball
 from optax.projections._projections import projection_non_negative
 from optax.projections._projections import projection_simplex
diff --git a/optax/projections/_projections.py b/optax/projections/_projections.py
index 3b70976d..1c34f879 100644
--- a/optax/projections/_projections.py
+++ b/optax/projections/_projections.py
@@ -277,3 +277,26 @@ def projection_l2_ball(pytree: Any, scale: float = 1.0) -> Any:
                       lambda pytree: pytree,
                       lambda pytree: otu.tree_scalar_mul(factor, pytree),
                       operand=pytree)
+
+
+def projection_linf_ball(pytree: Any, scale: float = 1.0) -> Any:
+  r"""Projection onto the l-infinity ball.
+
+  This function solves the following constrained optimization problem,
+  where ``x`` is the input pytree.
+
+  .. math::
+
+    \underset{y}{\text{argmin}} ~ ||x - y||_2^2 \quad \textrm{subject to} \quad
+    ||y||_{\infty} \le \text{scale}
+
+  Args:
+    pytree: pytree to project.
+    scale: radius of the ball.
+
+  Returns:
+    projected pytree, with the same structure as ``pytree``.
+  """
+  lower_tree = otu.tree_full_like(pytree, -scale)
+  upper_tree = otu.tree_full_like(pytree, scale)
+  return projection_box(pytree, lower=lower_tree, upper=upper_tree)
diff --git a/optax/projections/_projections_test.py b/optax/projections/_projections_test.py
index 23b05b38..f01185be 100644
--- a/optax/projections/_projections_test.py
+++ b/optax/projections/_projections_test.py
@@ -43,6 +43,7 @@ def setUp(self):
     self.fns = dict(
         l1=(proj.projection_l1_ball, otu.tree_l1_norm),
         l2=(proj.projection_l2_ball, otu.tree_l2_norm),
+        linf=(proj.projection_linf_ball, otu.tree_linf_norm),
     )
 
   def test_projection_non_negative(self):
@@ -196,7 +197,7 @@ def test_projection_l2_sphere(self, data_key, scale):
 
   @parameterized.product(
       data_key=['array_1d', 'array_2d', 'tree'],
-      norm=['l1', 'l2'],
+      norm=['l1', 'l2', 'linf'],
   )
   def test_projection_ball(self, data_key, norm):
     """Check correctness of the projection onto a ball."""