In　this　paper,　an　adaptive　sliding　mode　controller　is　designed　for　the　omnidirectional　mobile　robot　with　four　Mecanum　wheels　to　track　the　trajectory.　The　Mecanum　wheel　mobile　robot　has　been　widely　used　in　factories,　hospitals,　families　and　other　workspaces　because　of　its　omnidirectional　ability.　Consider　the　dynamic　model　of　the　omnidirectional　mobile　robot　based　on　Mecanum　wheel　with　uncertainties　and　external　disturbances,　a　neural　network　adaptive　sliding　mode　control　(NNASMC)　strategy　is　proposed,　which　combines　the　techniques　of　Radial　Basis　Function　(RBF)　neural　network　adaptive　control　method　and　sliding　mode　control　method.　Finally,　some　simulation　experiments　are　conducted　in　the　Matlab　environment.　Simulation　results　demonstrate　the　effectiveness　of　the　proposed　control　method.