We present in this paper numerical simulation results of the thermal radiative properties of a two-dimensional (2D) rectangular SiC grating atop a photonic crystal (PC). The results show that surface phonon polaritons (SPhPs) can be excited by both TE and TM waves when they are scattered by the 2D grating. Excitation of SPhPs, PC modes, and magnetic polaritons (MPs), and interactions between them give rise to great enhancement of the emissivity. Distinct effects of the grating geometry on the resonance of SPhPs, PC modes, and MPs were revealed, which suggest a way to effectively manipulate the emissivity by tuning the structure's geometry. Furthermore, the results indicate that quasi-diffuse emissivity of the structure can be obtained for both TE and TM waves.