Abstract: In order to solve updating core attributes of incremental condition attribute system, an equivalent binary discernibility matrix is proposed based on in-depth study firstly. And an algorithm for fast computing positive region in incremental condition attribute system is proposed by analyzing influence of increased condition attribute to the known positive region and binary discernibility matrix. Then, the updating core algorithm in incremental condition attribute system is presented. The algorithm computes binary discernibility matrix on the base of originally binary discernibility matrix by updating its portion and gets core attribute. Because the algorithm avoids computing from very beginning, so it improves the computing speed. The theoretical analysis and experimental results show the new algorithm is much more efficient and useful in computing.