The effect of group-velocity dispersion (GVD) and self-phase modulation (SPM) on the coherent pulse progression in mid-infrared (MIR) quantum-cascade lasers (QCLs) is investigated. The background saturable absorber (SA) effect is included in the study. In this case, the lasing pulses can be built up from the instable continuous wave (CW) operation condition related to both SA effect and GVD under the influence of a small initial disturbance. The theoretical model is built based on the Maxwell-Bloch formulism accounting for the couplings among the electric field, the polarization, and the population inversion. The pulse evolution in time-spatial domains is simulated by the finite difference method with prior nondimensionalization, which is necessary for convergent solution. We first studied the QCLs with ring cavity to illustrate the interplay between GVD and SPM effects. It is found that the anomalous GVD, which receives less attention in the study of QCL dynamics, can significantly narrow the spectrum splitting between side modes. The SPM can broaden the linewidth of the spectral modes. Their combined effects can lead the possibility of forming solitons. We also extended our study to the same QCL medium with a Fabry-Perot (FP) cavity. The additional effect of spatial-hole burning (SHB) is identified in results obtained.