diff --git a/core/src/main/scala/cats/Traverse.scala b/core/src/main/scala/cats/Traverse.scala
index b380f152297..dc85704e4c3 100644
--- a/core/src/main/scala/cats/Traverse.scala
+++ b/core/src/main/scala/cats/Traverse.scala
@@ -135,12 +135,21 @@ import simulacrum.typeclass
   override def map[A, B](fa: F[A])(f: A => B): F[B] =
     traverse[Id, A, B](fa)(f)
 
+  /**
+   * Akin to [[map]], but allows to keep track of a state value
+   * when calling the function.
+   */
+  def mapAccumulate[A, S, B](fa: F[A], init: S)(f: (S, A) => (S, B)): (S, F[B]) =
+    traverse(fa) { a =>
+      State(s => f(s, a))
+    }.run(init).value
+
   /**
    * Akin to [[map]], but also provides the value's index in structure
    * F when calling the function.
    */
   def mapWithIndex[A, B](fa: F[A])(f: (A, Int) => B): F[B] =
-    traverse(fa)(a => State((s: Int) => (s + 1, f(a, s)))).runA(0).value
+    mapAccumulate(fa, 0)((i, a) => (i + 1) -> f(a, i))._2
 
   /**
    * Akin to [[traverse]], but also provides the value's index in
@@ -206,10 +215,14 @@ object Traverse {
       typeClassInstance.sequence[G, B](self.asInstanceOf[F[G[B]]])
     def flatSequence[G[_], B](implicit ev$1: A <:< G[F[B]], G: Applicative[G], F: FlatMap[F]): G[F[B]] =
       typeClassInstance.flatSequence[G, B](self.asInstanceOf[F[G[F[B]]]])(G, F)
-    def mapWithIndex[B](f: (A, Int) => B): F[B] = typeClassInstance.mapWithIndex[A, B](self)(f)
+    def mapAccumulate[S, B](init: S)(f: (S, A) => (S, B)): (S, F[B]) =
+      typeClassInstance.mapAccumulate[A, S, B](self, init)(f)
+    def mapWithIndex[B](f: (A, Int) => B): F[B] =
+      typeClassInstance.mapWithIndex[A, B](self)(f)
     def traverseWithIndexM[G[_], B](f: (A, Int) => G[B])(implicit G: Monad[G]): G[F[B]] =
       typeClassInstance.traverseWithIndexM[G, A, B](self)(f)(G)
-    def zipWithIndex: F[(A, Int)] = typeClassInstance.zipWithIndex[A](self)
+    def zipWithIndex: F[(A, Int)] =
+      typeClassInstance.zipWithIndex[A](self)
   }
   trait AllOps[F[_], A]
       extends Ops[F, A]
diff --git a/laws/src/main/scala/cats/laws/TraverseLaws.scala b/laws/src/main/scala/cats/laws/TraverseLaws.scala
index 61bce31df46..46ba86761a3 100644
--- a/laws/src/main/scala/cats/laws/TraverseLaws.scala
+++ b/laws/src/main/scala/cats/laws/TraverseLaws.scala
@@ -106,6 +106,17 @@ trait TraverseLaws[F[_]] extends FunctorLaws[F] with FoldableLaws[F] with Unorde
     first <-> traverseFirst
   }
 
+  def mapAccumulateRef[A, S, B](fa: F[A], init: S, f: (S, A) => (S, B)): IsEq[(S, F[B])] = {
+    val lhs = F.mapAccumulate(fa, init)(f)
+
+    val rhsState = F.traverse(fa) { a =>
+      State(s => f(s, a))
+    }
+    val rhs = rhsState.run(init).value
+
+    lhs <-> rhs
+  }
+
   def mapWithIndexRef[A, B](fa: F[A], f: (A, Int) => B): IsEq[F[B]] = {
     val lhs = F.mapWithIndex(fa)(f)
     val rhs = F.traverse(fa)(a => State((s: Int) => (s + 1, f(a, s)))).runA(0).value
diff --git a/laws/src/main/scala/cats/laws/discipline/TraverseTests.scala b/laws/src/main/scala/cats/laws/discipline/TraverseTests.scala
index 2cbbdc7d1c8..7bb28c7c496 100644
--- a/laws/src/main/scala/cats/laws/discipline/TraverseTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/TraverseTests.scala
@@ -59,11 +59,12 @@ trait TraverseTests[F[_]] extends FunctorTests[F] with FoldableTests[F] with Uno
     EqYFM: Eq[Y[F[M]]],
     EqOptionA: Eq[Option[A]]
   ): RuleSet = {
-    implicit def EqXFBYFB: Eq[(X[F[B]], Y[F[B]])] =
+    implicit val EqXFBYFB: Eq[(X[F[B]], Y[F[B]])] =
       new Eq[(X[F[B]], Y[F[B]])] {
         override def eqv(x: (X[F[B]], Y[F[B]]), y: (X[F[B]], Y[F[B]])): Boolean =
           EqXFB.eqv(x._1, y._1) && EqYFB.eqv(x._2, y._2)
       }
+
     new RuleSet {
       def name: String = "traverse"
       def bases: Seq[(String, RuleSet)] = Nil
@@ -76,6 +77,7 @@ trait TraverseTests[F[_]] extends FunctorTests[F] with FoldableTests[F] with Uno
           "traverse traverseTap" -> forAll(laws.traverseTap[B, M, X] _),
           "traverse derive foldMap" -> forAll(laws.foldMapDerived[A, M] _),
           "traverse order consistency" -> forAll(laws.traverseOrderConsistent[A] _),
+          "traverse ref mapAccumulate" -> forAll(laws.mapAccumulateRef[A, M, C] _),
           "traverse ref mapWithIndex" -> forAll(laws.mapWithIndexRef[A, C] _),
           "traverse ref traverseWithIndexM" -> forAll(laws.traverseWithIndexMRef[Option, A, C] _),
           "traverse ref zipWithIndex" -> forAll(laws.zipWithIndexRef[A, C] _)
diff --git a/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala b/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala
index 5cc9d5dc68f..2ab357d5b8a 100644
--- a/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/TraverseSuite.scala
@@ -36,6 +36,19 @@ abstract class TraverseSuite[F[_]: Traverse](name: String)(implicit ArbFInt: Arb
     }
   }
 
+  test(s"Traverse[$name].mapAccumulate") {
+    forAll { (fa: F[Int], init: Int, fn: ((Int, Int)) => (Int, Int)) =>
+      val lhs = fa.mapAccumulate(init)((s, a) => fn((s, a)))
+
+      val rhs = fa.foldLeft((init, List.empty[Int])) { case ((s1, acc), a) =>
+        val (b, s2) = fn((a, s1))
+        (s2, b :: acc)
+      }
+
+      assert(lhs._2.toList === rhs._2.reverse)
+    }
+  }
+
   test(s"Traverse[$name].mapWithIndex") {
     forAll { (fa: F[Int], fn: ((Int, Int)) => Int) =>
       assert(fa.mapWithIndex((a, i) => fn((a, i))).toList === (fa.toList.zipWithIndex.map(fn)))