Based on the accuracy of the first-order Born approximation, the scattering properties of a spatially partially coherent plane-wave light incident on a quasi-homogeneous random medium were investigated. The analytical expressions for the spectral density and the spectral degree of coherence of the scattered field in the far zone were derived. The influence of the spatial coherence of the incident field and the properties of the scattering on the spectral density and the spectral degree of coherence of the scattered field was examined. Compared with a fully coherent light, the spectral density and the spectral degree of coherence of the field generated by scattering of a partially coherent light were analyzed. The results indicate that the spatial coherence of the incident light has an important role in the behavior of the spectral density of scattered field. With an increase of the correlation length of the GSM beam, the effective angular width of the spectral density of the scattered field decreases. The spectral degree of coherence of the scattered field increases with decreasing beam width of the incident light or effective radius of the medium. The scattered field is fully coherent when the appropriate choices of the effective radius and the correlation length of the medium, the spatial correlation length of the incident light are made.