To enhance the detection performance of weak targets against sea clutter, this paper proposes a hybrid detection method. This method integrates improved variational mode decomposition (IVMD) combined with wavelet packet multi-threshold decomposition (WPD), and a long short-term memory (LSTM) network optimized by the Harris Hawks optimization (HHO) algorithm. The IVMD, whose optimal parameters are determined adaptively by adaptive particle swarm optimization (APSO), is employed to precisely decompose the sea clutter signal into several intrinsic mode functions (IMFs). For the high-frequency IMFs containing strong noise, a multi-band wavelet packet decomposition and layered threshold denoising strategy is designed within the WPD framework to effectively suppress noise while preserving weak target characteristics. The Harris Hawks optimization algorithm is utilized to optimize the hyperparameters of the LSTM model, thereby enhancing its capability for nonlinear time-series modeling within the complex sea clutter environment. By combining phase space reconstruction with the denoised signals, the accuracy and anti-interference capability of target detection are significantly improved. Experiments using the real-world IPIX radar dataset from McMaster University, Canada, demonstrate that the proposed method markedly improves detection accuracy under both high and low signal-to-noise ratio conditions. Compared to traditional LSTM-based methods, the detection capability is improved by at least 35%.