Offshore ship-mounted cranes, as a typically nonlinear (multiple inputs and multiple outputs) MIMO system, have been extensively researched, aiming at their underactuated characteristics. Different from land-fixed cranes as well as traditional harbor cranes, offshore ship-to-ship crane systems work in two noninertial (ship) frames, while the target locations of the cargo are also inevitably influenced by the movements of the target ship. We established a new ship-to-ship crane frame, by improving the model of offshore ship-mounted cranes. By measuring the state of the target hull, a target trajectory about the load in a new noninertial frame is obtained. Then, we propose a (Proportional Integral) PD control theory-based anti-swing tracking control strategy for the coordinated offshore crane systems. Rigorous Lyapunov analysis ensures that the proposed controller enables the crane to transport the load to the specified target position while guaranteeing the elimination of residual pendulum angles. Furthermore, simulations are carried out to verify the effectiveness of the controller, demonstrating that the proposed coordinated tracking controller is able to quickly and accurately fulfil the control objectives of load transport and residual pendulum angle suppression, as well as having good robustness in the face of load variations and external perturbations.