Abstract: Attribute reduction of rough sets is an NP hard problem, but there is not a popular efficient algorithm presently. The attribute union concept based on the set theory and the attribute reduced algorithm based on this concept were presented. The algorithm translates the attribute reduction to find the attribute union, reducing the number of scanning the decision table and improving the reduced efficiency. The scanning strategy from bottom to top and with width priority can insure to find the minimal reduction. Also, an example was presented to describe the algorithm.