In this letter, a kind of metamaterial superstrate based on rectangular metallic grids is presented to enhance the directivity of patch antenna at two frequency bands for two orthogonal polarizations. According to the periodic boundary condition, the influences of its important geometry parameters are investigated in detail by simulating its unit cell. It is found that the transmission peak frequency is intimately related to the size of rectangular metallic grid. Then, a dual band dual polarization patch antenna with metamaterial is studied and compared with conventional patch antenna. It is demonstrated that by introducing the proposed metamaterial superstrate, the gain of the patch antenna is improved by 9.5 dB at 14.1 GHz for x polarization and 12 dB at 15.4 GHz for y polarization, respectively.