The transmission characteristics of optical waveguide ring resonator with tunable Mach-Zehnder interferometer (MZI) are analyzed. The formulas of the intensity and phase transfer functions are deduced according to the coupled-mode theory. It shows that the resonant frequencies shift range and the modulation power of Mach-Zehnder interferometer are heavily dependent on the parameters of Mach-Zehnder interferometer. An optimized design for ring resonator is demonstrated, the numerical ring modeling with the radius of 2 cm and the propagation loss of 0.08 dB/cm is performed around the central wavelength of 1550 nm, the resonant frequencies shift range is lower than 0.027 GHz, and the maximum notch depth is obtained, it means that the frequency modulator with small bandwidth can be used for the ring resonator and the finesse can be tuned with lower power.