In this paper, what we believe to be a novel method is proposed to suppress the fading effect of the phase-sensitive optical time domain reflectometer (Ф-OTDR) by using a phase-modulated optical frequency comb. In the Ф-OTDR system, intensity distributions of Rayleigh backscattering (RBS) light are different for pulsed probe lights with different central frequencies, therefore the locations of the fading points corresponding to signals of different frequencies are differently distributed, allowing the use of frequency division multiplexing to suppress the fading effects. In the experimental system of this paper, a continuous light in the form of a frequency comb is firstly generated through phase modulation. It is then modulated into a pulsed probe light and injected into the sensing fiber to produce different RBS intensity distributions. Finally, the extracted phase is processed by using the amplitude evaluation method, so that the distorted phase can be eliminated. Fading suppression is achieved using our system, and the effect of suppression is evaluated. By using an equal-amplitude optical frequency comb containing seven frequency components, the fading probability density of the system is dramatically reduced from the range of 5.49%-9.83% to 0.08%. Compared with the conventional system using a single acoustic-optic modulator to generate the frequency shift, the method proposed in this paper features a larger modulation bandwidth and more flexible frequency combination scheme to better suppress the fading effect. This method does not sacrifice the response bandwidth of the system, and the phase delay can be precisely controlled, which helps to fully suppress the fading effect.