Quadrature-polarimetric synthetic aperture radar (quad-pol SAR) has extensive applications, including climate zones classification, extraction of surface roughness, soil moisture mapping, moving target indication, and rice mapping. Hybrid quad-pol SAR ameliorates the range ambiguity performance of conventional quad-pol SAR. However, the azimuth ambiguity of its cross-polarized (cross-pol) echo signals is serious, limiting the swath width of SAR. Therefore, this paper proposes a spaceborne weighted amplitude modulation (WAM) full-polarimetric (full-pol) SAR system, and it can suppress the azimuth ambiguity of hybrid quad-pol SAR. The performance boost of the azimuth ambiguity by the two imaging modes of the proposed SAR system is detailed and evaluated with the L-band system parameters. Moreover, the chirp scaling algorithm (CSA) is adopted to execute scene simulations for the two imaging modes. The results indicate that the proposed SAR system can effectively suppress the azimuth ambiguity of hybrid quad-pol SAR and verify the theoretical analysis.