In this paper, we study query suggestion diversifcation for timeaware queries, where query suggestions are diversifed from multiple dimensions (e.g., topic and time). More precisely, we introduce the method of Time-aware Diversifed Query Suggestion (TDQS) which ensures that the generated suggested queries indicate possible time points in which a searcher who issued the original query may be interested. Preliminary experiments on AOL query log demonstrate that our proposed method can signifcantly improve the diversity and relevance effectiveness for time-aware queries in comparison with two state-of-the-art methods.