The rule learning algorithm on continuous attributes space is studied in this paper. First, thepurpose and the importance of studying rule learning algorithm on continuous attributes space are briefly introduced, and then some basic concepts in the theory of rule learning are extended to the continuous attributes space. On this basis, the authors study the problem to divide continuous attributes space, and prove that the problem of min dividing continuous attributes space is a NP hard problem. The concepts of information entropy and infinite normed apply to the problem of dividing continuous attribute space and a new algorithm of dividing continuous attribute space based on the function of information entropy are presented. At last, a rule learning algorithm on continuous attributes space is presented and the data results of the experiments are given.