A broadband microstrip patch antenna with dual-polarization is presented in the paper. There are four feed-lines and a cavity-backed ground plane in the antenna. The patch is electromagnetically coupled by these feed-lines. The phase offset of the two feeding ports located symmetrically relative to the center of the patch is 180°, which affords a solution to improve the polarization purity and the degree of isolation simultaneously. The cavity is used as another radiator for enhancing the bandwidth. The antenna is optimized by the particle swarm optimization (PSO) algorithm. The simulated results show a bandwidth of 61% (active VSWR<;2) and good radiation patterns.