Novel analytical expressions for the cross-spectral density function of a Gaussian Schell-model pulsed (GSMP) beam propagating through atmospheric turbulence are derived. Based on the cross-spectral density function, the average spectral density and the spectral degree of coherence of a GSMP beam in atmospheric turbulence are in turn examined. The dependence of the spectral degree of coherence on the turbulence strength measured by the atmospheric spatial coherence length is calculated numerically and analyzed in depth. The results obtained are useful for applications involving spatially and spectrally partially coherent pulsed beams propagating through atmospheric turbulence.