Area Under the ROC Curve (AUC) is a widely used metric for measuring classification performance. It has important theoretical and academic values to develop AUC maximization algorithms. Traditional methods often apply batch learning algorithm to maximize AUC which is inefficient and unscalable for large-scale applications. Recently some online learning algorithms have been introduced to maximize AUC by going through the data only once. However, these methods sometimes fail to converge to an optimal solution due to the fixed or rapid decay of learning rates. To tackle this problem, we propose an algorithm AdmOAM, Adaptive Moment estimation method for Online AUC Maximization. It applies the estimation of moments of gradients to accelerate the convergence and mitigates the rapid decay of the learning rates. We establish the regret bound of the proposed algorithm and implement extensive experiments to demonstrate its effectiveness and efficiency.