Efficiently salvaging shipwrecks is of the utmost importance for safeguarding shipping safety and preserving the marine ecosystem. However, traditional methods find it difficult to salvage shipwrecks in deep water. This article presents a novel salvage technology that involves multiple hydraulic claws for directly catching and lifting a 2500-ton shipwreck at 600 m depth. To ensure lifting stability, a semi-active heave compensation (SAHC) system was employed for each lifter to mitigate the effects of sea waves. However, the response delays arising from the hydraulic, control, and filtering systems resist the heave compensation performance. Predicting the barge motion to mitigate measuring and filtering delays and achieve leading compensation is necessary for the salvage. Therefore, a multivariate long short-term memory (LSTM) based neural network was trained to forecast the barge’s heave and pitch motions, exhibiting satisfactory results for the next 5 s. According to the results of numerical simulations, the proposed LSTM-based motion predictive SAHC system demonstrates remarkable effectiveness in compensating for shipwreck motion.