Dialogue systems are increasingly integrated into mental health support to help clients facilitate exploration, gain insight, take action, and ultimately heal themselves. For a dialogue system to be practical and user-friendly, it should be client-centric, focusing on the client's behaviors. However, existing dialogue systems publicly available for mental health support often concentrate solely on the counselor's strategies rather than the behaviors expressed by clients. This can lead to the implementation of unreasonable or inappropriate counseling strategies and corresponding responses from the dialogue system. To address this issue, we propose PsyChat, a client-centric dialogue system that provides psychological support through online chat. The client-centric dialogue system comprises five modules: client behavior recognition, counselor strategy selection, input packer, response generator intentionally fine-tuned to produce responses, and response selection. Both automatic and human evaluations demonstrate the effectiveness and practicality of our proposed dialogue system for real-life mental health support. Furthermore, we employ our proposed dialogue system to simulate a real-world client-virtual-counselor interaction scenario. The system is capable of predicting the client's behaviors, selecting appropriate counselor strategies, and generating accurate and suitable responses, as demonstrated in the scenario.