In　this　paper,　we　propose　an　optimal　entanglement　concentration　protocol　(ECP)　for　partially　entangled　cluster　states　with　the　help　of　the　weak　cross-Kerr　nonlinearity.　We　can　obtain　the　maximally　entangled　cluster　states　assisted　with　the　projection　measurements　on　the　additional　photons.　The　protocol　is　based　on　optical　elements,　single　polarization　photons,　cross-Kerr　nonlinearity,　and　the　conventional　photon　detectors,　which　are　feasible　with　existing　experimental　technology.　Numerical　simulation　demonstrates　that　by　iterating　the　entanglement　concentration　process　times,　the　ECP　has　the　approximate　maximal　success　probability　100　%.　Moreover,　the　present　protocol　is　also　suitable　for　partially　entangled　-photon　cluster　states　concentration.　All　these　advantages　make　this　protocol　more　efficient　and　more　convenient　than　others　in　the　applications　in　quantum　communication.