The Mamyshev cavity based on multi-cascade nonlinear broadening and offset filtering is used to propose a synchronous spectral overlapping multi-wavelength fiber laser. The single-cavity ring structure solves the problems of gain competition and difficulty in synchronization output of traditional multi-wavelength lasers. Through numerical simulation, the output of four-wavelength pulses with central wavelengths of 1035, 1040, 1045 and 1050 nm is realized. The spectral width of each pulse is 7 nm (greater than the interval between adjacent central wavelengths), the peak power (before external linear compression) is 0.9--1.0 kW, and the pulse width is about 0.28 ps. By optimizing the filter, the corresponding multi-wavelength output is discussed, and the influence of wavelength arrangement order on transmission function and system efficiency is analyzed.