A numerical method for structural dynamic topology optimization and sensitivity analysis is presented by using RKPM. In this paper, the relative density of node and maximum fundamental eigenfrequency is respectively chosen as design variable and the objective function, and then the mathematical model for dynamic topology optimization based on RKPM is built. During the process of modeling, some effective measures are taken to dispose the multi-eigenvalues and localized modes. Subsequently, the sensitivity analysis equation is proposed by using Direct Differentiation Method. Finally, by integrating the above sensitivity analysis with Optimality Criteria method, the dynamic topology optimization of an example is performed successfully. Numerical example shows that both checkboards and localized eigenmodes do not occur during topology optimization, and it indicates the proposed method is valid.