Attribute reduction is an important problem in an information system. The paper proposed a novel method to reduce the redudant attributes in an incomplete information system based on rough set theory. The method introduce the concepts such as upper-approximate relationship and lower-approximate relationship, equivalence relationship, tolerance relationship, attribute significance and so on, to calculate the core attributes and use the attribute significance as heuristic knowledge to reduce attributes set according to dependence between the conditonal attributes and decision attributes in the information system. Experiment results show that the algorithm is simple and effective.