Conical beam antenna plays a significant role in providing stable access to satellite signals for moving communication terminals. Although metasurfaces have been used to generate conical beams, most of them can only reflect conical beams with identically distributed and mirror-symmetric phase responses for left-hand circular polarization and right-hand circular polarization, which can hinder the dual-polarization applications of metasurfaces. In this study, a metasurface is designed to independently manipulate dual-polarized excitations in broadband. To achieve the broadband control of conical beams, broadband conditions for both geometric and propagation phases are developed. Differently, metasurface designed in this study consists of three types of distinguishingly shaped elements, which can provide more degree of freedom in dual-polarization broadband design. In addition, a design method is developed for metasurface to generate the cone angle tailorable conical beams. Via fabricating a metasurface following the proposed method, the designed metasurface is verified in theorem, simulation, and experiment that it can generate desired conical beams with tailored divergent angles and phase responses covering a bandwidth from 12.5 GHz to 17 GHz.