We report the influence of two spatial incident angles on a terahertz polarizer, which is based on an aluminum slab with a center slit flanked by symmetrically distributed parallel grooves on both sides. Experimental results show that the polarizer shows narrow bandpass filtering effect with a very small divergence angle at normal incidence, which is very suitable for terahertz communication, and the extinction ratio (ER) can be achieved above 20 dB in the frequency band between 0.3 and 0.36 THz due to the excitation of spoof surface plasmon. As the structure rotates around the slit direction (β), the transmission peak will split into two and degrade quickly and the ER decreased down to 20 dB for β=10° at peak position. Rotating along grating period direction (γ) shows better tuning performance. The tuning frequency window can reach from 0.3 to 0.36 THz to promise an ER above 20 dB as γ is smaller than 25°.