An efficient central or off-axis current drive is necessary for the steady-state operation of tokamak fusion reactors. The fast wave branch in the frequency range above two times the lower hybrid resonance frequency at high density, the so-called lower hybrid fast wave (LHFW), could be such an efficient current drive scheme in high density and high temperature of reactor-grade tokamak plasmas. This is because it has a higher parallel wave electric field for efficient Landau damping, compared to the fast wave branches in other frequency ranges, and it can more deeply penetrate high density plasmas than the slow wave in the same frequency range. An experimental study has been carried out to confirm the feasibility, in collaboration with Korea Atomic Energy Research Institute, Seoul National University, KwangWoon University, and Korea Accelerator and Plasma Research Association, in VEST. The results show that plasma current can be driven by the fast electrons generated by the LHFW. The details are reported including the theoretical background and RF system as well as the experiment results.