In order to exceed the limitations of LEM2（Learning from Examples Module,Version 2） algorithm in processing incomplete information system,an improved LEM2 rule-induction algorithm is proposed,with the qua-lity and efficiency of rule induction being both improved.Then,based on the set pair theory,the set pair situation tolerance relation and the generalized rough set model based on the tolerance relation are introduced in the incomplete information system,and the model is combined with the LEM2 algorithm to improve the quality of rule induction.Moreover,the redundant attribute-value pair set is defined,by deleting which from the candidate attribute-value pair sets during the rule induction,the converse elimination action is successfully avoided,the convergence is accelerated and the efficiency of rule induction is improved.Finally,some simulation experiments are conducted.The results verify the effectiveness of the improved LEM2 algorithm in the rule induction of incomplete information system.