Through the transfer matrix method, we demonstrated a special polarizer integrated with the functions of narrow bandpass (NBP) and narrow transmission-angle (NTA) filtering at normal incidence in a stack of two one-dimensional defective photonic crystals (PCs). One of the PCs is made of an isotropic dielectric media, while the other PC is made of anisotropic media. The key point in designing the stack is to set the central frequencies of the defect modes of the two sub-PCs to be the same for one polarization at normal incidence, but different for oblique incidence or for other polarizations, so that the stack structure could have the functions of three elements: a polarizer, an NBP filter, and an NTA filter.