Nonreciprocal thermal radiation represents an innovative approach to radiative heat transfer that overcomes the symmetric reciprocity constraints imposed by Kirchhoff's law. However, most existing nonreciprocal thermal radiation devices are limited to single polarization and typically necessitate large angles and significant magnetic fields. This paper presents a dual-band dual-polarization nonreciprocal thermal emitter made up of periodic arrays of silicon cylinders hollowed, a magneto-optical material layer, and a metallic plate. Rigorous coupled-wave analysis is employed to examine the structural parameters and the efficiency. Results demonstrate that the efficiencies of the two nonreciprocal bands for transverse electric (TE) and transverse magnetic (TM) polarizations exceed 90 % when subjected to a 1 T magnetic field and an incident angle of 5°. The underlying physical mechanism of strong nonreciprocity is elucidated through an investigation of coupled mode theory and the distributions of electromagnetic fields. Additionally, the validity of the computational results is corroborated using the finite element method. Furthermore, the impact of various parameters on nonreciprocity is analyzed. Compared to traditional nonreciprocal thermal emitters, the proposed emitter effectively reduces reliance on both magnetic field strength and incident angle, significantly enhancing its practical applicability in the field of energy harvesting.