Electro-optic-modulator (EOM) based Mach-Zehnder (M-Z) interferometer is a novel method of controlling the carrier envelope offset frequency (f₀). It is achieved by adjusting the envelop of the pulse, while keeping the carrier frequency unchanged. In this paper, the polarization control device involved in this method is simulated, and the influences caused by the deviation of the optical axis of the wave plate on the polarization direction and the degree of output laser are analyzed. An optical axis calibration method is proposed to reduce the influence caused by the deviation of optical axis of wave plate. The effects of pump current and EOM based M-Z interferometer on f₀ and the beat note (f_b) between the comb and the laser are compared with each other. The experimental results show that the effect of changing the pump current on f_b is 7 MHz, when the f₀ adjustment quantity is 9 MHz. Under the same f₀ adjustment quantity, the influence of EOM based M-Z interferometer on f_b is 0.2 MHz, which is only 1/35 of the influence of pump current. Therefore, it is verified that EOM based M-Z interferometer can effectively reduce the interference to f_b. It provides a technical means to narrow the line width of optical comb by using f_b to lock repetition rate (f_r) .