Currently, commercial search engines have implemented methods to suggest alternative Web queries to users, which helps them specify alternative related queries in pursuit of finding needed Web pages. In this paper, we address the Web search problem on related queries to improve retrieval quality by devising a novel search rank aggregation mechanism. Given an initial query and the suggested related queries, our search system concurrently processes their search result lists from an existing search engine and then forms a single list aggregated by all the retrieved lists. In particular we propose a generic rank aggregation framework which considers not only the number of wins that an item won in a competition, but also the quality of its competitor items in calculating the ranking of Web items. The framework combines the traditional and random walk based rank aggregation methods to produce a more reasonable list to users. Experimental results show that the proposed approach can clearly improve the retrieval quality in a parallel manner over the traditional search strategy that serially returns result lists. Moreover, we also empirically investigate how different rank aggregation methods affect the retrieval performance.