The improved Rayleigh-Ritz method was extended to the analysis of bending vibration characteristics of Mindlin plates in arbitrary shapes. The domain of displacement test function was extended to the rectangular region outside the curve region, and the improved Fourier series was selected as the test function. The complex boundary conditions were simulated by adopting the linear springs whose stiffness is adjustable. The numerical method was introduced to disperse the boundary edges and by summing up the elastic potential energy of each micro section the elastic potential energy of the whole boundary was obtained. Then, the problems of complex boundary conditions of curved edges brought by arbitrary shape problems can be solved. The equation was es- tablished based on the energy variation principle and Mindlin theory. By comparing the results of present method of the straight edge and curved edge plates with the results of the reference and the finite element results, the accuracy of this method is proved, which provides reference for the practical engineering problems.