Ocean thermal energy conversion (OTEC) provides a feasible solution for sustainable and stable power supply in remote islands. In this paper, a thermodynamic model of the OTEC system is developed to study the dynamic response of power output and superheating degree to manipulated variables. Afterward, a control strategy of load following for the island OTEC system is proposed. Finally, two controllers, MPC and PI, are designed and compared under fast and slow load changes as well as disturbance rejection test. The results indicate that the power output of OTEC system is sensitive to the speed of working-fluid pump, reaching the adjustment range of 14.7 kW when the nominal speed decreases by 30%. In addition, model predictive control (MPC) shows better performance in both rapid and slow load-change modes. Especially, in the rapid load-change mode, the MPC controller could always keep the evaporator outlet superheating in the range of 2–4.5 °C, while the PI controller may introduce no superheat that may cause liquid impact. Both MPC and PI controller can stabilize the power output at the set point under one day's measured disturbance, while MPC controller makes the superheating degree of evaporator outlet within smaller temperature fluctuations (<0.2 °C).