This article proposes a new strategy for individual blade pitch control to regulate power production while simultaneously alleviating structural loads on spar-type floating offshore wind turbines. Individual blade pitch control types of algorithms for offshore wind turbines are sparse in the literature though there are expected benefits from experience on such types of controllers for onshore wind turbines. Wind turbine blade pitch actuators are primarily used to maintain the rated power production at the above-rated wind speeds, and therefore, control algorithms are usually developed only to regulate power production. The scope of reducing structural loads using individual pitch control has been proven to be very promising over the last decade, and numerous individual pitch control algorithms have been proposed by researchers. However, reduction in structural loads often results in a degradation in power production and regulation. Furthermore, improving power regulation often has a detrimental effect on the floating platform motion. In this article, a new control strategy is proposed to achieve the two competing objectives. The proposed controller combines a low-authority linear-quadratic (LQ) controller with an integral action to reduce the 1P (once per revolution) aerodynamic loads while regulating power production using the same pitch actuators that are traditionally used only to optimize power production. The proposed controller is compared against the baseline controller (BC) used by the state-of-the-art wind turbine simulator FAST using a high-fidelity aeroelastic offshore wind turbine model. Numerical results show that the proposed controller offers improved performance in optimizing power production and reducing wind turbine and platform loads compared with the BC over an envelope of wind-wave loading environment.