This paper is concerned with the free vibration analysis of an annular plate with boundary conditions of simply supported-free, clamped-free and free-free, respectively. Exact solutions for the natural frequency and mode of an annular plate can be obtained by solving the differential equation but other methods such as the Rayleigh-Ritz method and the finite element method can be also used. In this research, we applied the Independent Coordinate Coupling Method(ICCM) to the annular plate and prove that the ICCM can accurately predict the natural frequency and mode shape of the annular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of plate with a hole compared to the Rayleigh-Ritz method and the finite element method.