Current crawler-based search engines usually return a long list of search results containing a lot of noise documents. By indexing collected documents on topic path in taxonomy, taxonomy-based search engines can improve the search result qualities. However, the searches are limited to the locally compiled databases. In this paper, we propose an adaptive web search method to improve the search result qualities enabling the users to search in many databases existing in the web space. The method has a characteristic that combines the taxonomy-based search engines and a machine learning technique. More specifically, we construct a rule-based classifier using pre-classified documents provided by a taxonomy-based search engine based on a selected context category on its taxonomy, and then use it to modify the user query. The resulting modified query will be sent to the crawler-based search engines and the returned results will be presented to the user. We evaluate the effectiveness of our method by showing that the returned results from the modified query almost contain documents that will be categorized into the selected context category.