A meshless local Petrov-Galerkin method for the elastic dynamic analysis of a nonhomogeneous moderately thick plate is presented in this paper. The discretized system equation of the moderately thick plate is obtained using a locally weighted residual method. It uses a radial basis function coupled with a quadratic polynomial basis function as a trial function and a quartic spline function as a test function of the weighted residual method. The shape function has the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions. In computational procedures, variations of material properties in the considered domain are modelled by adopting proper material parameters at Gauss points in integrations. Examples show that the presented method can give quite accurate results to elastic dynamic problems of the nonhomogeneous moderately thick plate.