Based on the composite surface scattering model, the analytical formulas for Doppler shift and bandwidth of radar echoes return from time-varying sea surface are derived. In our derivations, the influences of the tilt modulation, the shadow and the curvature of large-scale undulating waves are all taken into account for achieving more reasonable results. Comparisons between the theoretical results and direct numerical simulations demonstrate that the analytical formulas can significantly improve the simulated results. And the effects of the tilt modulation, the shadow and the curvature on Doppler spectral properties are discussed in detail. From the simulated results, it is found that the predicted Doppler shifts are always larger in HH-polarization than in VV-polarization due to the tilt modulation of large-scale waves. In addition, at low-grazing angles, the shadow of large-scale waves results in a rapid increase of the predicted Doppler shift, and on the contrary maks the bandwidth narrower.