Mooring systems are a significant capital cost of a floating wave energy converter and their premature failure negatively impacts operational costs. Excessive peak loads and accumulated fatigue damage can lead to failure, so these factors are cost drivers in wave energy converter design. Here, the potential to reduce platform motion and mooring loads through modification of the power take-off (PTO) control are investigated. An approximate velocity tracking control strategy is implemented with a linear quadratic regulator design method using differential weighting of system states. It is demonstrated that the controller can be tuned to capture similar mean power to an optimally tuned, passively damped system while significantly reducing mooring line cyclic loading. The relative accumulated fatigue damage in the mooring lines in a high energy sea-state is found to be reduced by between 43% and 92% as a result of using the approximate velocity tracking control strategy.