Graphene-based metasurfaces have emerged as promising photoelectric devices for dynamically controlling the polarization and wavefront of electromagnetic waves. A series of novel graphene-based metasurfaces consisting of split-ring resonators are proposed and researched. A dynamically tunable broadband converter of polarization states composed of periodically patterned graphene split-rings for linearly polarized waves is achieved in terahertz regime. By designing different geometrical parameters, the resonators indicate 2π of smooth phase modulation in a broadband frequency regime. Based on the phase profile design, a polarization beam splitter and a transmission-type focusing metasurface in a broadband frequency regime are both demonstrated successfully. Furthermore, the efficiency of these metasurfaces is dynamically tunable by modulating the gate voltage to change the Fermi energy (Ef) of graphene. This work may offer a potentially effective method to instruct the design of tunable polarization converter and wavefront-controlling devices.