Conversational Agents (CAs) acting as peer supporters have been widely studied and demonstrated beneficial for people’s mental health. However, previous peer support CAs either are user-initiated or follow predefined rules to initiate the conversations, which may discourage users to engage and build relationships with the CAs for long-term benefits. In this paper, we develop ComPeer, a generative CA that can proactively offer adaptive peer support to users. ComPeer leverages large language models to detect and reflect significant events in the dialogue, enabling it to strategically plan the timing and content of proactive care. In addition, ComPeer incorporates peer support strategies, conversation history, and its persona into the generative messages. Our one-week between-subjects study (N=24) demonstrates ComPeer ’s strength in providing peer support over time and boosting users’ engagement compared to a baseline user-initiated CA. We report users’ interaction patterns with ComPeer and discuss implications for designing proactive generative agents to promote people’s well-being.