In this paper, we develop a face recognition system with a rejection mechanism for imposter or unseen subjects. In order to boost the recognition rate and provide the promising rejection accuracy, a margin-enhanced space is derived by reweighting the LSDA space via explicitly imposing the constraint of the k-NN classification rule. In this space, not only the local discriminant structure of data can be extracted but the enhanced pairwise distance can be used to model the acceptance and rejection likelihood probability. According to the Bayes decision rule, the unseen subject can be rejected if the likelihood ratio is smaller than the estimated threshold. Note that the rejection performance based on the likelihood ratio is more tolerable than the pre-defined distance only. Experimental results show that the proposed system not only yields the higher recognition rate than other subspace learning methods but also provides the promising rejection accuracy on the challenging databases of various lighting conditions and facial expression.