A good concept drifting stream classifier should have the following two characteristics: 1) sensitive to the new concept when concept drifts; 2) have stable high accuracy when concept is stable. Most published methods and algorithms may succeed in one aspect while neglecting the other. In this paper, we proposed an adaptive ensemble classifier for concept drifting stream classification which focuses on both the above two aspects called AEC. Our AEC includes two stages: the online stage and the offline stage, and three phases: classifier updating, ensemble classifiers reconstruction and component classifier subset selection for final decision. We take a new online bagging classification model that is based on incremental learner such as Naive Bayes classifier and can keep enough history information and create good diversity between different component classifiers. Then we take an offline scheme to do the ensemble reconstruction and ensemble subset selection: that is to drop certain number of classifiers periodically and use only a portion of the whole ensemble, the combination of which may yield better accuracy to make classification. Experiment justifies the superiority of our model in both accuracy and sensitivity in the concept drifting environment.