A staggered metasurface structure that consists of double-periodic supercells with eight different V-shaped antennas is proposed and its properties are studied theoretically and experimentally. The calculation shows that co-polarized transmission and cross-polarized anomalous refraction can be obtained when the transverse electric light is incident vertically. The phase difference of anomalous refraction can be changed and its amplitude can be regulated by adjusting the transverse misalignment distance between two periodic supercell units. The experimental results show that, when the 4.3 THz light is vertically incident on the samples with two supercells staggered by 0, 2, 4 and 6 V-shaped antenna unit cells, the anomalous refraction intensities are 3.6%, 1.7%, 0.7%, and 1.9% of the incident light intensity, respectively, which is consistent with the calculated results.