Based on the coherence theory of non-stationary fields, the spectral degree of polarization of two-dimensional spatially and spectrally partially coherent electromagnetic Hermite-Gaussian pulsed beams propagating in free space is studied and analyzed numerically. It is shown that the spectral degree of polarization of electromagnetic Hermite-Gaussian pulsed beams depends on the beam order, spatial correlation length, temporal coherence length and the position of the field point. The on-axis spectral degree of polarization, which is independent of the beam order and the position of the field point, tends to a fixed value when the spatial correlation length tends to zero or infinite. The on-axis spectral degree of polarization increases with the increase of temporal coherence length, and decreases with the increase of pulse duration when the beam order is large or the propagation distance is long. The larger the beam order is, the more times the spectral degree of polarization P=0 appears on cross section.