Based on the propagation law of partially coherent beams and Fourier transform, the analytical expressions for the spectral intensity and spectral degree of coherence of focused spatially and spectrally partially coherent Hermite-Gaussian (H-G) pulsed beams are derived and used to study the spatial correlation properties in the focal region. It is shown that the spectral degree of coherence depends on the spatial correlation length, temporal coherence length and beam order. As the temporal coherence length decreases, the spectral degree of coherence decreases, whereas the temporal coherence length does not contribute to the spatial distribution of the spectral degree of coherence. An increase of the beam order results in an oscillatory behavior of the spectral degree of coherence, which becomes more prominent with the increase of beam order or the decrease of spatial correlation length.