Attribute reduction is an important issue of rough set theory. It has been proven that finding the minimal reduct of an information system is a NP-hard problem, so is finding the minimal reduct of an incomplete information system. Main reason of causing NP-hard is combination problem. In this paper, we theoretically study an attribute reduction algorithm. It based on results of Chen Degang et al in consistent and inconsistent covering decision system. The time complexity of this algorithm is O(|delta||U|2). An illustrative example is provided that shows the application potential of the algorithm