Computing the core is an important research issue in the rough set. The method for computing the core based on improved discernibility matrix, which was presented by Yang Ming, is studied. The example shows that the method is still imperfect in some aspects. In order to improve the efficiency of computing the core, the definition of a simplification discernibility matrix and the method of computing the core are provided. It is proved that the core acquired from the method is equivalent to the core based on the positive region. Based on this,a computing core algorithm is designed, and its time complexity is max {O(|C||U|),O(|C||U/C||U′1|)},and its space complexity is O(|C||U/C||U′1|). The experimental results show that the algorithm is not only effective and efficient, but also suitable for processing huge data efficiently.