In classification problems, major methods focus on the minimization of the classification error rate. This is not always a suitable performance measure when sample numbers of classes are biased. In this case, the area under the Receiver Operating Characteristic curve (AUC) is an effective performance measure. However in general, direct construction of classifier which maximizes the AUC is difficult because its definition is not differentiable and not concave. In this paper, we extend the concept of AUC using a smooth concave function and propose a new performance measure, U-AUC. Based on the new measure, we propose a Boosting type algorithm and discuss statistical properties of the algorithm. In addition, we demonstrate validity of the proposed method by experiments with dataset in UCI repository.