Peer code review, or manual review of submitted code, which is an effective way to reduce defects and improve quality, has been widely adopted by open source communities and many software development organizations, such as Github. In the GitHub community, code reviews are an important part of its pull-based software development model. Open source projects often have hundreds or thousands of candidate reviewers, recommend suitable reviewers for code review is a very valuable and challenging work. Based on the data analysis of real open source projects, it is found that the response time of review is a common problem, which will extend the review cycle and reduce the enthusiasm of participants. Existed work did not take the response time into account. Therefore, the code reviewer recommendation problem is proposed with response time constraint, and then the code reviewer recommendation method (MOC2R) is proposed based on multi-objective optimization by maximizing the experience of code reviewers, maximizing the response probability within the time window, and maximizing the activity of staff within the latest time. The experiments are conducted based on data from six open source projects, and the results show that under different time window constraints (2h, 4h, 8h), Top-1 accuracy rate is 41.7%~61.5%, Top-5 accuracy rate is 66.5%~77.7%, significantly better than the two commonly used and industry-leading baseline methods, and all three objectives contributed to the recommendation among which the response probability within the time window contributes the most. The proposed method can further enhance code review efficiency, improve the activity of the open source community.