In order to improve the user search experience, Query Suggestion, a technique for generating alternative queries to Web users, has become an indispensable feature for commercial search engines. However, previous work mainly focuses on suggesting relevant queries to the original query while ignoring the diversity in the suggestions, which will potentially dissatisfy Web users' information needs. In this paper, we present a novel unified method to suggest both semantically relevant and diverse queries to Web users. The proposed approach is based on Markov random walk and hitting time analysis on the query-URL bipartite graph. It can effectively prevent semantically redundant queries from receiving a high rank, hence encouraging diversities in the results. We evaluate our method on a large commercial clickthrough dataset in terms of relevance measurement and diversity measurement. The experimental results show that our method is very effective in generating both relevant and diverse query suggestions.