We propose a three layered metal-graphene-metal metasurface to investigate the controllable linear asymmetric transmission and perfect polarization conversion in THz regime, by using the finite-difference time-domain (FDTD) method. An on-to-off control of asymmetric transmission and perfect polarization conversion is achieved by changing the Fermi energy of graphene from 0.8 eV to 0 eV. We present the electric field distribution and Fabry-Perot-like cavity model to analyze the working mechanisms. By gradually shifting the Fermi energy of graphene, two functions are realized, i.e., controllable linear asymmetric transmission and controllable total transmission with near perfect polarization conversion.