Temporal information plays important roles in Web search, as Web pages intrinsically involve crawled time and most Web pages contain time keywords in their content. How to integrate temporal information in Web search engines has been a research focus in recent years, among which some key issues such as temporal-textual indexing and temporal information extraction have to be first studied. In this paper, we first present a framework of temporal-textual Web search engine. And then, we concentrate on designing a new hybrid index structure for temporal and textual information of Web pages. In particular, we propose to integrate B+-tree, inverted file and a typical temporal index called MAP21-Tree, to handle temporal-textual queries. We study five mechanisms to implement a hybrid index structure for temporal-textual queries, which use different ways to organize the inverted file, B+-tree and MAP-21 tree. After a theoretic analysis on the performance of those five index structures, we conduct experiments on both simulated and real data sets to make performance comparison. The experimental results show that among all the index schemes the first-inverted-file- then-MAP21-tree index structure has the best query performance and thus is an acceptable choice to be the temporal-textual index for future time-aware search engines.