Based on the angular spectrum theory, we establish a propagation model for vortex beam in reflection at an air-glass interface in the paraxial approximation, and investigate the cross polarization effects. When the horizontal polarization vortex beam is incident at different angles, the cross polarization component of the reflected beam shows a double-peak intensity distribution which is similar to the first-order Hermite-Gaussian mode. The distribution of horizontal polarization component is similar to that of the incident beam, and will show a double-peak intensity distribution which is perpendicular to the distribution of cross polarization components at the Brewster incidence. For the incident beam with arbitrary linear polarizations, we find that the polarized direction of cross polarization component is not perpendicular to the incident polarized direction, but exhibits an interesting rotational characteristic. The physical nature of this phenomenon is attributed to the different reflection coefficients of parallel and perpendicular polarizations. Experimental results agree well with our theoretical analysis.