Users often have imprecise ideas when searching the autonomous Web databases and thus may not know how to precisely formulate queries that lead to satisfactory answers. This paper proposes a novel flexible query answering approach that uses query relaxation mechanism to present relevant answers to the users. Based on the user initial query and the data distribution, we first speculate how much the user cares about each attribute and assign a corresponding weight to it. Then, the initial query is relaxed by adding the most similar attribute values into the query criteria range. The relaxation order of attributes specified by the query and the relaxed degree on each specified attribute are varied with the attribute weights. The first attribute to be relaxed is the least important attribute. For the relevant result tuples, they are finally ranked according to their satisfaction to the initial query. The efficiency of our approach is also demonstrated by experimental result.