In multi-wave and multi-component seismic exploration, accurate matching between P-waves (PP) and converted waves (PS) is a prerequisite for joint interpretation and inversion. However, PS waves usually have low signal-to-noise ratio, insufficient resolution, and strong differences in dynamic and kinematic characteristics compared with PP waves. Therefore, traditional matching methods show limited generalization under complex geological conditions. To address this problem, an artificial intelligence matching method for PP and PS waves is proposed based on a cross-domain training strategy. First, the PS wave was preliminarily aligned to the PP-wave time domain by trace-wise layered resampling. Then, an MS-SeiUnet waveform matching network was constructed. A Multi-Scale Residual Attention Block (MSRA Block) was introduced to capture multi-level geological features. Multi-scale feature information was also integrated to achieve fine-grained waveform matching of PS waves. To solve the problem of limited training samples, a cross-domain driven training strategy was further proposed. In this strategy, the Adaptive Matching Pursuit (MP) algorithm was used to decompose original broadband PP waves. Low-frequency atomic components were constructed from the decomposed PP waves. The high-frequency waveform information of PP waves was then used to drive the fine-grained matching of PS-wave features. The proposed method is applied to ocean-bottom node (OBN) multi-wave seismic data from an offshore area. The results show high consistency between well logs and seismic data. The fine-grained waveform matching of converted waves is achieved. A solid foundation is also provided for subsequent high-precision multi-wave seismic exploration and reservoir development.