Using the coherence theory of non-stationary fields and the method of Fourier transform, the spectral properties of spatially and spectrally partially coherent Gaussian Schell-model pulsed (GSMP) beams in fused-silica glass medium are studied and analyzed numerically. It is shown that the spectral shift takes place, which depends on the position of the field point, spatial correlation length, temporal coherence length and dispersive property of medium, as GSMP beams propagate in fused-silica glass medium. The on-axis spectrum is blue-shifted, and the relative spectral shift increases with increasing propagation distance, and decreases as the spatial correlation length and temporal coherence length increases, and then approaches an asymptotic value. The dispersive property of medium plays an important role in the spectral properties of spatially and spectrally partially coherent beams.