We introduce a new metasurface structure for controlling the polarization of light by leveraging a well-harmonized combination of graphene and dielectric. The proposed metasurface is composed of an array of rectangular pillars laterally sandwiched by ribbons of graphene. Being able to dynamically change the polarization state of the reflected wave, the proposed structure is employed to realize a switchable polarization converter, which is able to act as a reflector (co-polarizer)/right-hand circular (RHC) quarter-wave plate or RHC/cross/left-hand circular (LHC) polarizer based on its design configuration. The reflected amplitude in all states of functionality is remarkably high. It is also shown that, for some states, the proposed polarization converter demonstrates broad working bandwidth both spatially and spectrally. Therefore, it could find applications in tera-hertz imaging, sensing, and communication and also could be easily used to realize other beam-shaping functionalities such as lensing. (C) 2018 Optical Society of America