We consider a highly anisotropic metamaterial structure, composed of parallel metal nanostripes, and show that a thin layer of the material can be used as a tunable partial polarizer. The transmittance of the structure for TE-polarized waves depends strongly on the incidence angle, while for TM-polarized waves, it stays high and essentially constant. In particular, using the structure, the degree of polarization of a partially polarized or unpolarized light can be tuned by changing the incidence angle. The TE-wave transmittance drops from, c.a., 1 to 0 when the incidence angle increases by 5 deg only, owing to the presence of an unusual higher-order odd-symmetric TM mode that we have revealed in the structure. The tuning can be made smoother by introducing another layer of a similar metal-nanostripe structure on top of the first one. The new design allows the TE-wave transmittance to decrease gradually towards 0 with the incidence angle increasing from 0 to about 30 deg. Our structures serve as an essential optical component for studies involving partially polarized light.