In this paper, a 2D periodic structure made of tungsten (W) grating patch on a thin Al2O3 spacer and an opaque W film is proposed, as a broadband selective thermal emitter. We numerically investigated the spectral emissivity of the structure from the deep by finite-difference time-domain method. Geometric parameters effects on the emissivity are discussed and the mechanisms of magnetic polaritons in the structure are further analyzed in detail. In addition, by adding another metal-dielectric stack upon the pre-existing grating structure, the emissivity of the composite structure can be further enhanced, and the normal emissivity exceeds 0.95 in the wavelength range of 0.65-1.95 μm, some even close to unity. Furthermore, the composite structures are found to exhibit insensitivity to polar angle and polarization.