Dirty data brings new challenges for data management. Current methods of dirty data management are mainly data cleaning. Such methods have limitations when dealing with in applications. In some systems, dirty data has to be tolerated. Therefore, the management of databases with dirty data becomes an important issue. The crucial problem is to obtain query result with a clean degree satisfying clean requirement of applications from databases with dirty data. From the aspect of dirty data management, a data model for dirty databases is presented in this paper. This paper proposes the representation of dirty data, data operators for dirty data and the computation method of clean degree of tuples with support of data operation. The equivalent transformation rules for query expressions on dirty data and the preliminary implementation of the data model are also discussed in this paper.