A novel fiber ring resonator based on Mach-Zehnder (M-Z) interferometer is proposed. Its transmission function is theoretically analyzed using the transfer matrix method. The expression for the full width at half maximum of the transmission spectrum is also derived. Numerical simulations show that transmission spectrum has the periodic narrow stopband filtering characteristic. The influence of phase difference between the two arms of M-Z interferometer and coupling coefficient on the transmission spectrum is also analyzed. The results are of important significance to its actual processing and improvement of filtering characteristic.