A new method, to the best of our knowledge, to measure frequencies of received microwave signal based on an optical frequency comb (OFC) and a photonic multi-channel receiver is proposed and simulated. The measurement system mainly includes a seed laser, an OFC generator composed of two cascaded Mach-Zehnder modulators, a frequency shifter, an intensity modulator, a wavelength-division demultiplexer, photodiodes (PDs), and electrical filters. Two sets of beat signals need to be obtained in the measurement process. By analyzing the two sets of beat signals, multiple frequency components of the microwave signal can be measured at a time. The validity of the proposed scheme is verified by VPI simulation software. It is shown that microwave frequencies within dozens of gigahertz can be precisely measured, and factors affecting the frequency measurement range are also studied.