A simple scheme for the realization of the terahertz (THz) fundamental-mode tunable closed-stopband composite right/left-handed leaky-wave antennas (CRLH LWAs) is presented. The proposed CRLH LWAs are reconstructed by graphene-based coplanar waveguide (CPW) transmission line supercells. Their shunt inductance achieved by narrow graphene strips of two unit cell structures are halfed. The CRLH LWAs are designed and confirmed by numerical simulations. They also exhibit frequency-scanning behaviors at THz with narrower bandwidth than that of the conventional graphene-based fundamental-mode CPW unit cell CRLH LWAs at THz. Besides, the LWAs also exhibit strong tunable characteristics and achieve the closed-stopband condition more effectively. Therefore, the proposed supercell CRLH LWAs could further improve the performance of the beam-steering antennas at THz.