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Imbalanced data classification is a challenging problem frequently encountered in many real-world applications. Traditional classification algorithms are generally designed to maximize overall accuracy; therefore, their effectiveness tends to be impeded by imbalanced data. Similar to other traditional classifiers, naive Bayes (NB) sometimes fails at predicting minority instances owing to its sensitivity to class distribution. To cope with this challenge, we proposed RankOptAUC NB (RNB), a novel attribute weighting method for the NB. In the proposed method, learning a weighted NB classifier was formulated as a nonlinear optimization problem with the objective of maximizing the area under the ROC (AUC). The optimization formulation enabled the RNB method to select important variables by simply adding a regularization term to the objective function. We also provided theoretical evidence that, based on the AUC metric, the proposed method improved the performance of a weighted NB classifier. The results of numerical experiments conducted using 30 real-world datasets proved that the proposed scheme successfully determined the optimal attribute weights for imbalanced data classification.