Object detection can be posted as those classification tasks where the rare positive patterns are to be distinguished from the enormous negative patterns. To avoid the danger of missing positive patterns, more attention should be payed on them. Therefore there should be different requirements for False Reject Rate (FRR) and False Accept Rate (FAR) , and learning a classifier should use an asymmetric factor to balance between FRR and FAR. In this paper, a normalized asymmetric classification error is proposed for the task of rejecting negative patterns. Minimizing it not only controls the ratio of FRR and FAR, but more importantly limits the upper-bound of FRR. The latter characteristic is advantageous for those tasks where there is a requirement for low FRR. Based on this normalized asymmetric classification error, we develop an asymmetric AdaBoost algorithm with variable asymmetric factor and apply it to the learning of cascade classifiers for face detection. Experiments demonstrate that the proposed method achieves less complex classifiers and better performance than some previous AdaBoost methods.