We herein report a linear polarizer based on a 2D array of substrate integrated waveguide cavities, which can convert an arbitrary linearly polarized (LP) incident wave into an outgoing LP wave in a specified polarization direction with constant transmittance. Two orthogonal slots etched on the front surface of the cavity are utilized to couple a wave of arbitrary polarization into the cavity, while another slot on the back side helps to couple the field out along a desired polarization direction. Microwave experiments are performed as a proof of concept. The proposed polarizer exhibits very good performance with stable transmittance as 50% and a polarization extinction ratio over 45 dB. The new polarizer is potentially useful in novel polarization-selective devices that are immune to the polarization direction of an incident plane wave.