Peer relationships play important roles in middle-school students' individual development. Peer support is indispensable in computer-supported learning contexts. This study is designed to explore the connection between perceived peer support and deeper learning, while examining the mediating role of computer self-efficacy and perceived classroom mastery goal structure. 412 middle school students in northwest China were sampled by constructing the structural equation model (SEM) in this study. The results displayed that perceived peer support had no direct positive predictive effect on deeper learning. Computer self-efficacy completely mediated in perceived peer support and deeper learning. Perceived classroom mastery goal structure completely mediated in perceived peer support and deeper learning. Computer self-efficacy and perceived classroom mastery goal structure played a chain mediating effect in perceived peer support and deeper learning. These findings not only deepen our comprehend of the internal mechanism about peer relationships in promoting deeper learning, but also provide constructive suggestions on how to maintain positive peer relationships among students in computer-supported teaching situations, so as to improve students' digital literacy and skills from the dimension of satisfying their social emotional needs.