An improve Fourier series method is employed to analyze the free vibration of tapered plates with general elastic boundary support, in which the vibration displacements is sought as the linear combination of a double Fourier cosine series and auxiliary series functions. The use of these supplementary functions is to solve the discontinuity problems which encountered in the displacement partial differentials along the edges, and the displacement can meet the displacement and stress boundary conditions. Boundary conditions are physically realized with the uniform distribution of transverse and rotational springs on each boundary edge. Different boundary conditions can be directly obtained by changing the stiffness of springs. Then the Rayleigh-Ritz method based on Hamilton’s principle can give the matrix equation which is equivalent to the governing differential equations of the tapered plate, and the eigenvalues and eigenvectors can be obtained by solving the matrix equation. Finally the numerical results and the comparisons with FEA as well as those reported in the literature are presented to validate the correct of the method.