In this paper, we present an AUC (i.e., the Area Under the Curve of Receiver Operating Characteristics (ROC)) maximization based learning algorithm to design the classifier for maximizing the ranking performance. The proposed approach trains the classifier by directly maximizing an objective function approximating the empirical AUC metric. Then the gradient descent based method is applied to estimate the parameter set of the classifier. Two specific classifiers, i.e. LDF (linear discriminant function) and GMM (Gaussian mixture model), and their corresponding learning algorithms are detailed. We evaluate the proposed algorithms on the development set of TRECVID'051 for semantic concept detection task. We compare the ranking performances with other classifiers trained using the ML (maximum likelihood) or other error minimization methods such as SVM. The results of our proposed algorithm outperform ML and SVM on all concepts in terms of its significant improvements on the AUC or AP (average precision) values. We therefore argue that for semantic concept detection, where ranking performance is much interested than the classification error, the AUC maximization based classifiers are preferred.