Metasurfaces, a new kind of artificial subwavelength structures, have exhibited unprecedented capabilities in wavefront control of electromagnetic waves. Currently, a series of active metasurfaces have been explored for engineering applications in anomalous refraction, ultrathin flat lens, holograms, and vortex beam generation, However, to date, most reported metasurfaces are mainly concentrated on active control on the polarization conversion and wavefront of circular polarized waves. Here, graphene-functionalized metasurfaces consisting of metallic double split ring resonators integrated with graphene (G-DSRRs) are proposed to actively control polarization conversion and wavefronts of linearly polarized waves at the terahertz region. By carefully designing spatially phase profile, anomalous reflection of linearly cross-polarized terahertz waves is demonstrated in a broadband range of frequencies. Moreover, the amplitude of the anomalous reflection terahertz wave can be dynamically tuned by varying Fermi energy via electrically doping graphene. Based on the tunable graphene-functionalized metasurface, several polarization conversion metasurface devices including vortex beam generators, invisibility cloaks, and metalens, are successfully designed and numerical results show that their amplitudes can be actively tuned to a significant extent by doping graphene. Therefore, such graphene-functionalized metasurfaces may have potential applications in THz telecommunications, high-resolution terahertz displays, and advanced THz imaging devices.