A broadband dual-polarized single-layer 1-bit unit cell is proposed for achieving the independently controllable dual-beam reflectarray antenna. The unit cell independently provides two-state phase compensation for two orthogonally linearly-polarized waves. The 180-degree reflective phase difference between the two states is achieved by tuning the magnetic resonance of State 0 and the electrical resonance of State 1. With its two resonances close to each other, the unit cell has a reflective phase difference of 180±20 degrees between two states over a broad bandwidth of 27.2-51.1 GHz. The cross-polarization levels of below -30 dB ensure the high isolation between two polarizations. Using the proposed dual-polarized unit cells, a 1-bit dual-beam reflectarray antenna is designed and excited by a dual-polarized horn to show the ability of independently controlling two orthogonally linearly-polarized waves. At 33 GHz, the beams direct to -15 degrees and 20 degrees for the feeding of horizontally and vertically polarized port, respectively. The 1.5-dB gain bandwidth is greater than 20% for both polarizations. The proposed dual-polarized reflectarray antenna with independently controllable 1-bit dual beams provides an alternative design for the multiuser multiple-input multiple-output applications.