We focused on the effects of group-velocity dispersion (GVD) on the coherent pulse progression in mid-infrared (MIR) quantum-cascade lasers (QCLs). Comparison of GVD effects on the two kinds of typical QCL cavities, i.e., FP and ring cavities, brings insight into the interaction between the GVD and the spatial hole burning (SHB) effect which is only supported by FP cavities but not ring cavities. The theoretical model is built based on the Maxwell-Bloch formulism accounting for two-way propagations of electric field and polarization as well as 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 a convergent solution. Results predict that the SHB could broaden the QCL gain bandwidth and induce additional side modes closely around the central lasing mode with an intensity more pronounced than that of GVD associated side modes. Moreover, owing to the SHB, the lasing instability caused by GVD is weaker in a FP cavity than a ring cavity.