Greater efficiency, and the relatively more straightforward structure of DC microgrids, give rise to DC microgrid technology for renewable energy integration. In this work, an intelligent controller is proposed for a DC microgrid that comprises a wave energy converter and a hybrid energy storage system. A wave energy converter oscillating in heave, which drives a linear permanent magnet generator as a power take-off (PTO) mechanism, is used in this study. Additionally, HESS, consisting of battery and supercapacitor, is used for power quality improvement and DC bus voltage regulation. The DC bus connects with each system component through dedicated power converters, with the WEC device using an active rectifier, and the HESS (battery and ultra-capacitor) utilising two bidirectional DC-DC converters. In the paper, a model is derived for the individual components of the microgrid. Then, Lyapunov-based intelligent controllers are designed for the power converters in such a way that they achieve the control objectives. An energy management strategy is also used to ensure proper power-sharing among the HESS components. The controller system is then simulated in a MATLAB/Simulink environment, and the result shows that the proposed controllers achieve the desired control objectives and perform well under various operating conditions.