Time plays important roles in Web search, because most Web pages contain temporal information and a lot of Web queries are time-related. How to integrate temporal information in Web search engines has been a research focus in recent years. However, traditional search engines have little support in processing temporal-textual Web queries. Aiming at solving this problem, in this paper, we concentrate on the extraction of the focused time for Web pages, which refers to the most appropriate time associated with Web pages, and then we used focused time to improve the search efficiency for time-sensitive queries. In particular, three critical issues are deeply studied in this paper. The first issue is to extract implicit temporal expressions from Web pages. The second one is to determine the focused time among all the extracted temporal information, and the last issue is to integrate focused time into a search engine. For the first issue, we propose a new dynamic approach to resolve the implicit temporal expressions in Web pages. For the second issue, we present a score model to determine the focused time for Web pages. Our score model takes into account both the frequency of temporal information in Web pages and the containment relationship among temporal information. For the third issue, we combine the textual similarity and the temporal similarity between queries and documents in the ranking process. To evaluate the effectiveness and efficiency of the proposed approaches, we build a prototype system called Time-Aware Search Engine (TASE). TASE is able to extract both the explicit and implicit temporal expressions for Web pages, and calculate the relevant score between Web pages and each temporal expression, and re-rank search results based on the temporal-textual relevance between Web pages and queries. Finally, we conduct experiments on real data sets. The results show that our approach has high accuracy in resolving implicit temporal expressions and extracting focused time, and has better ranking effectiveness for time-sensitive Web queries than its competitor algorithms.