The Maxwell-Bloch equations describing the class-B lasers were obtained by the Hisonberg equation for the single-mode homogenously broadened travelling laser. The laser system, in which the modulated pump intensity was studied in detail. By numerical calculation, the sequence of positive period-doubling vifurcation and the sequency of reverse chaotic band were observed.In the chaotic band, some of the period windows were found. The temporary behavior of the system was in quasi-period instabilities and chaos motion. In some regions of the parameters, the system lost its stabilities and directly transited into chaos from one limit cycle.