Based on the coherence theory, the non-stationary optical fields with the complex degree of coherence (CDOC) are expanded from stationary fields, and random pulse sources with temporal multi-complex degree of coherence (TMCDOC) is introduced. Theoretical model for the random pulse sources with TMCDOC is established. The analytical transmission formulas for the temporally spectral density and TMCDOC of the pulse beam spreading through dispersive media are derived and its propagation properties in dispersive media are explored. One can find from the numerical results that the TMCDOC pulse beam will evolve from a single pulse at the source plane into N subpulses in the far field or produce far field spectral density with flat-topped profiles. The variation of the non-trivial phase of the CDOC can regulate the propagation angle of the TMCDOC pulse beam. Moreover, in case of the propagation in dispersive media with chirp coefficient s < 0, the TMCDOC pulse beam will exhibit self-focusing process, and its coherence curves will be reversed from the clockwise rotation in the near field to anticlockwise rotation in the far field.