A broadband and high-efficieny bi-layer metasurface is proposed in this paper. The unit cell of the metasurface is formed by symmetrically etching two cross-type metal patches on both sides of a dielectric plate. Furthermore, the two metal patches have a displacement of half a period along the y-axis. By employing the displacement, the transmission bandwidth of the bi-layer metasurface is significantly expanded. In order to obtain a physical insight into bandwidth broadening, a π-type equivalent circuit that presents the electromagnetic coupling between within the bi-layer metasurfaces is successfully extracted to investigate the influence of electromagnetic coupling on transmission performance. The results show that by shifting the metal patches along the y-axis by half a period, the coupling impedance (Z₁₂ or Z₂₁) of bi-layer metasurface can be significantly modified, which further changes the electromagnetic coupling of the bi-layer metasurface. Correspondingly, the impedances Z_p and Z_s in the π-type circuit are changed to approximately meet the resonant condition of circuit in broadband, resulting in the bandwidth expansion of the proposed device. By using Pancharatnam-Berry phase theory, we redesign the proposed metasurface unit cell into a broadband orbital angular momentum generator. The simulation and measurement results verify that the bi-layer metasurface can convert a left-hand circularly polarized wave into a right-hand circularly polarized wave carrying orbital angular momentum in a frequency range between 11 GHz and 12.8 GHz, demonstrating the performance of device.