The theory, method, and experimental studies on mode-locked free-electron laser (FEL) have been of great interests in the world. In this paper, we propose a method to generate mode-locked multi-color free-electron laser radiation pulses based on the electron beam phase space beating. Utilizing an electron beam with head-tail energy chirp and the two modulator-chicane setups in the Shanghai Soft X-ray free-electron laser facility (SXFEL), multiple current pulse trains can be formed and mode-locked multi-color free electron laser pulses can be generated. The simulation results indicate that, with the help the 264 nm seed laser, bunching factor at the 18^th harmonic of the seed laser can be formed and ultimately mode-locked multi-color FEL radiation pulse with a central wavelength of approximately 14.58 nm can be generated. This study is of great significance for the development of the mode-locked FEL in China and the performance improvement of the SXFEL facility.