The non-inductive current drive in low toroidal beta (β) steady-state superconducting tokamak-1 (SST-1) is obtained using slow waves or Lower Hybrid waves (LHW). If β of the plasma is increased either by increasing the plasma parameters (density/temperature) or by decreasing the toroidal magnetic field, the non-inductive current drive may be supported by Fast Waves (FWs), as wave accessibility is limited for slow waves at these high β plasmas. Non-inductive current drive using FWs is explored for these high β plasmas to identify the optimized parameters (operating frequency and parallel refractive index (n||)) of the fast wave. The studies indicate that FWs may be launched with an operating frequency of 0.5 GHz RF source and n|| around 4 in SST-1 plasma. The GENRAY code is employed to carry out detailed studies on Fast Wave Current Drive (FWCD) analysis using ray tracing techniques. Computational studies on FWCD are carried out where central electron density (ne0) and central electron temperature (Te0) of 6×1019m−3 and 3 keV respectively is assumed. The FWCD displays central depositions of RF power and is attributed to fast radial propagation compared to the parallel propagation along the toroidal magnetic field, resulting in ray transits with large number of reflections. The off-axis current drive in SST-1 plasma requires reduced radial penetration of the wave and demands unrealistic plasma parameter in terms of β. However, for SST-2 plasmas, having enhanced plasma parameters (βN∼1.8), it is found that if FWs are launched with n||∼3 and f∼1.5 GHz, the radial penetration of the wave is impeded and single pass absorption in toroidal direction is observed, thus providing conducive condition for off axis current drive. It indicates that FWs would drive plasma current of 11 kA/MW at ρ∼0.7 for ne0∼2.2×1020m−3 and Te0∼7.7 keV values.