In the Semantic Web, RDF (Resource Description Framework) and RDF Schema are commonly used to describe metadata. There are a great many RDF data in current web, therefore, efficient storage and retrieval of large RDF data sets is required. So far, several RDF storage and query system are developed. According to the inference strategy they used, they can be classified into two categories, one exclusively use forward chaining strategy; the other exclusively use backward chaining strategy. In most cases, the query performance of the former is superior to that of the latter. However, in some cases, the disadvantage of larger storage space may at some point outweigh the advantage of faster querying. Further, the existing systems that exclusively use forward chaining strategy have not yet presented a good solution to the deletion operation by now. In this paper, we design a RDF storage and query framework with flexible inference strategy, which can combine forward and backward chaining inference strategies. In addition, a new solution to the deletion operation is also given within our framework. The feasibility of our framework is illustrated by primary experiments.