The majority of marine current conversion technologies are based on permanent magnet synchronous generators (PMSG) due to its numerous advantages such as high-power density, low cost, and favorable electricity production. However, nonlinear properties of the generator and parameter uncertainties, makes the controller design more than a simple challenge. This paper proposes a new adaptive passivity-based (PB) modified super twisting algorithm (PBSTA) for control performance improvement (low tracing errors, fast convergence response, robustness) of a PMSG based marine current energy conversion system under swell effect and parameter uncertainties. The proposed approach combines a new PB current control (PBCC) with a new adaptive modified super twisting algorithm through a fuzzy logic supervisor. A new adaptive fractional order PID (FO-PID) controller is introduced to design the desired dynamics of the system. The main contributions and motivation of this work include the extraction of maximum power from the tidal current, integrating it to the grid and making the closed loop system passive. This is possible by reshaping system energy and introducing a damping term that compensates the nonlinear terms by a damped way and not by cancellation. Two steps are needed to design the proposed controller: the first step includes the derivation of reference current based on the reference torque using adaptive FO-PID. In the second step, the overall control law is computed by the proposed PBSTA. The exponential stability and error convergence of the proposed controller are analytically proven. The developed controller is tested under parameter variations and it is compared to benchmark nonlinear control methods such as sliding mode. Extensive investigation under MATLAB/Simulink, demonstrates clearly that the proposed technique provides higher efficiency and robustness over the benchmark nonlinear control methods.