diff --git a/jax/_src/custom_batching.py b/jax/_src/custom_batching.py
index 3184003d7701..41a4512e07a1 100644
--- a/jax/_src/custom_batching.py
+++ b/jax/_src/custom_batching.py
@@ -237,3 +237,34 @@ def to_vmap_over_extra_batched_dims(primals, tangents):
                          initial_style=True)
 mlir.register_lowering(custom_vmap_p, mlir.lower_fun(
     custom_vmap_impl, multiple_results=True))
+
+
+# -- custom vmap applications
+
+
+def tree_split(mask, tree):
+  lhs = tree_map(lambda l, x: x if l else None, mask, tree)
+  rhs = tree_map(lambda l, x: None if l else x, mask, tree)
+  return lhs, rhs
+
+def tree_merge(mask, lhs_tree, rhs_tree):
+  return tree_map(lambda l, x_l, x_r: x_l if l else x_r,
+                  mask, lhs_tree, rhs_tree)
+
+def sequential_vmap(f):
+  f = custom_vmap(f)
+
+  @f.def_vmap
+  def rule(axis_size, in_batched, *args):
+    del axis_size
+
+    def to_map(mapped_args):
+      args = tree_merge(in_batched, mapped_args, bcast_args)
+      return f(*args)
+
+    mapped_args, bcast_args = tree_split(in_batched, list(args))
+    out = jax.lax.map(to_map, mapped_args)
+    out_batched = tree_map(lambda _: True, out)
+    return [out], [out_batched]
+
+  return f
diff --git a/jax/custom_batching.py b/jax/custom_batching.py
index d8f6317eb8d2..7e18733f2001 100644
--- a/jax/custom_batching.py
+++ b/jax/custom_batching.py
@@ -15,4 +15,5 @@
 # flake8: noqa: F401
 from jax._src.custom_batching import (
   custom_vmap,
+  sequential_vmap,
 )
diff --git a/tests/api_test.py b/tests/api_test.py
index e50ef7098cfa..033b7d49dc82 100644
--- a/tests/api_test.py
+++ b/tests/api_test.py
@@ -42,6 +42,7 @@
 import jax.numpy as jnp
 from jax import float0, jit, grad, device_put, jacfwd, jacrev, hessian
 from jax import core, lax
+from jax import custom_batching
 from jax._src import api, dtypes
 from jax.core import Primitive
 from jax.errors import UnexpectedTracerError
@@ -6962,6 +6963,48 @@ def rule(axis_size, in_batched, xs):
     self.assertAllClose(jit(api.vmap(f))(xs), api.vmap(f)(xs))
     self.assertAllClose(api.vmap(jit(f))(xs), api.vmap(f)(xs))
 
+  def test_sequential_vmap_basic(self):
+    @custom_batching.sequential_vmap
+    def f(x):
+      return x + 1.
+
+    def vmap_ref(xs):
+      return lax.map(f, xs)
+
+    xs = jnp.arange(3.)
+    jaxpr = api.make_jaxpr(api.vmap(f))(xs)
+    jaxpr_ref = api.make_jaxpr(vmap_ref)(xs)
+
+    self.assertEqual(str(jaxpr), str(jaxpr_ref))
+
+  def test_sequential_vmap_nary_same_batching(self):
+    @custom_batching.sequential_vmap
+    def f(x, y):
+      return x + y
+
+    def vmap_ref(xs, ys):
+      return lax.map(lambda args: f(*args), (xs, ys))
+
+    xs, ys = jnp.arange(3.), 4. + jnp.arange(3.)
+    jaxpr = api.make_jaxpr(api.vmap(f))(xs, ys)
+    jaxpr_ref = api.make_jaxpr(vmap_ref)(xs, ys)
+
+    self.assertEqual(str(jaxpr), str(jaxpr_ref))
+
+  def test_sequential_vmap_nary_mixed_batching(self):
+    @custom_batching.sequential_vmap
+    def f(x, y):
+      return x + y
+
+    def vmap_ref(xs, y):
+      return lax.map(lambda x: f(x, y), xs)
+
+    xs, y = jnp.arange(3.), 4.
+    jaxpr = api.make_jaxpr(api.vmap(f, in_axes=(0, None)))(xs, y)
+    jaxpr_ref = api.make_jaxpr(vmap_ref)(xs, y)
+
+    self.assertEqual(str(jaxpr), str(jaxpr_ref))
+
 
 class CustomApiTest(jtu.JaxTestCase):
   """Test interactions among the custom_{vmap,jvp,vjp,transpose,*} APIs"""