Community Question Answering (CQA) has increasingly become an important service for people asking questions and providing answers online, which enables people to help each other by sharing knowledge. Recently, with accumulation of users and contents, much concern has arisen over the efficiency and answer quality of CQA services. To address this problem, question routing has been proposed which aims at routing new questions to suitable answerers, who have both high possibility and high ability to answer the questions. In this paper, we formulate question routing as a multi-objective ranking problem, and present a multi-objective learning-to-rank approach for question routing (MLQR), which can simultaneously optimize the answering possibility and answer quality of routed users. In MLQR, realizing that questions are relatively short and usually attached with tags, we first propose a tagword topic model (TTM) to derive topical representations of questions. Based on TTM, we then develop features for each question-user pair, which are captured at both platform level and thread level. In particular, the platform-level features summarize the information of a user from his/her history posts in the CQA platform, while the thread-level features model the pairwise competitions of a user with others in his/her answered threads. Finally, we extend a state-of-the-art learning-to-rank algorithm for training a multi-objective ranking model. Extensive experimental results on real-world datasets show that our MLQR can outperform state-of-the-art methods in terms of both answering possibility and answer quality.