The ultrathin graphene metasurface is proposed and analyzed as a cloaking shell for cylindrical objects with the aim of wideband tunable scattering cancellation in terahertz (THz) spectrum. This mantle cloak is structured by periodic array of graphene nanopatches. In this paper, it is analytically shown that the metasurface reactance can be tuned from inductive to capacitive, as a function of the graphene's Fermi energy and dimensions of nanopatches, that provide the possibility of cloaking both dielectric and conductor cylinders. The appropriate Fermi energy and dimensions are obtained by optimization. To provide wideband invisibility, we use inhomogeneous graphene nanopatches, that we could significantly increase the 3-dB bandwidth approximately 8 times more than the homogeneous metasurface. These resultes have great interest for efficient invisibility, low noise THz sensing and communication systems and networks.