We investigate the coherence properties of a cosine-Gaussian-correlated Schell-model (CGSM) pulse scattered from a quasi-homogeneous random medium. Further, we derive an analytic expression to obtain the temporal coherent degree of the scattered field in the far-zone and investigate the influences of the pulse parameters and properties of the medium on the temporal coherent degree of the scattered field. The numerical calculations denote that the cosine order plays an important role in the distribution of temporal coherent degree of the scattered field. Furthermore, we compare the coherent characteristics, similarities, and differences between a CGSM pulse and a Gaussian Schell-model pulse.