Existing legal judgment prediction methods usually only consider one single case fact description as input, which may not fully utilize the information in the data such as case relations and frequency. In this paper, we propose a new perspective that introduces some contrastive case relations to construct case triples as input, and a corresponding judgment prediction framework with case triples modeling (CTM). Our CTM can more effectively utilize beneficial information to refine the encoding and decoding processes through three customized modules, including the case triple module, the relational attention module, and the category decoder module. Finally, we conduct extensive experiments on two public datasets to verify the effectiveness of our CTM, including overall evaluation, compatibility analysis, ablation studies, analysis of gain source and visualization of case representations.