Variations of marine current speed can lead to strong fluctuations in the power extracted by a marine current turbine (MCT). During short-time period, swell effect is the main cause for the current speed variations. Conventional tip speed ratio Maximum Power Point Tracking (MPPT) algorithm will require the MCT to accelerate or to decelerate frequently under swell effect, which can cause severe fluctuations in the generator power. This paper focuses on power smoothing control of a PMSG-Based MCT system. A modified MPPT algorithm with filter strategy is proposed in generator-side control to use the system inertia for smoothing the fluctuation of generator power. When the current speed is over rated value, the power limitation control will be applied. In the second step, Supercapacitor (SC) Energy Storage System (ESS) is added to compensate the residual power fluctuations. Simulations of a 1.5 MW direct-driven grid-connected MCT system are carried out. The results demonstrate that the association of the generator-side filter strategy with the SC ESS system achieves a smoothed power injected to the grid in case of swell disturbances.