This paper proposes a beamforming design for millimeter-wave (mmWave) backhaul systems with dualpolarization antennas in uniform planar arrays (UPAs). The proposed design method optimizes a beamformer to mimic an ideal beam pattern, which has flat gain across its coverage, under the dominance of the line-of-sight (LOS) component in mmWave systems. The dual-polarization antenna structure is considered as constraints of the optimization. Simulation results verify that the resulting beamformer has uniform beam pattern and high minimum gain in the covering region.