In harsh sea conditions, a shipborne stable platform is required for smooth offshore operations due to the serious sway of the ship. Aiming at this requirement, a new active heave compensation system consisting of an Inertial Measurement Unit (IMU) and a Stewart platform is designed to compensate for the roll, pitch and heave motions of the ship. Firstly, the system is modeled in detail. Then, the task space controller is designed based on forward kinematics for the Stewart to eliminate the coupling errors of six links. To obtain accurate and real-time solutions of forward kinematics, a novel method based on Beetle Antennae Search (BAS) algorithm is proposed. In order to compensate for external disturbances, an improved adaptive control strategy based on Radial Basis Function Neural Network (RBFNN) with fading factors is designed. Finally, the effectiveness and rationality of the proposed method are validated by simulation and physical experiment. The maximum compensation errors of the proposed method are reduced by 70% in row/pitch and 40% in heave as compared to the traditional method.