The rough set theory is proved to be an effective method for attribute reduction. By now, many heuristic attribute reduction algorithms have been proposed, where the information entropy-based attribute reduction algorithms have received much attention. To solve the problems of the current information entropy-based attribute reduction algorithms, a new model of information entropy, approximate decision entropy, is defined, and an approximate decision entropy-based attribute reduction algorithm, called ADEAR, is also proposed. Some experiments are carried out on several UCI data sets. The experimental results show that ADEAR algorithm can obtain smaller reducts and higher classification accuracies than the current algorithms, and the computational cost of ADEAR algorithm is relatively low.