As the development of tidal turbines attracts more and more attention in recent years, reliable design and efficient control of tidal turbines are becoming increasingly important. However, the majority of existing tidal turbines still utilize traditional fixed ratio geared transmissions and the associated control designs focus on simple feedback controllers that use measurements or possibly estimates of the turbine itself or current local tidal profile. Therefore, the measurement and control are inevitably affected by the inherent delay with respect to the current tidal speeds. This paper proposes a novel tidal turbine with continuously variable speed hydrostatic transmissions and a nonlinear predictive controller that uses short-term predictions of the approaching tidal speed field to enhance the maximum tidal power generations when the tidal speed is below the rated value. The controller is designed based on an offline finite-horizon continuous time minimization of a cost function, and an integral action is incorporated into the control loop to increase the robustness against parameter variations and uncertainties. A smooth second order sliding mode observer is also designed for parameter estimations in the control loop. A 150 kW tidal turbine with hydrostatic transmission is designed and implemented. The results demonstrate that the averaged generator power increases by 6.76% with this preview based nonlinear predictive controller compared with a classical non-predictive controller.