Cross-modal metric learning (CML) deals with learning distance functions for cross-modal data matching. The existing methods mostly focus on minimizing a loss defined on sample pairs. However, the numbers of intraclass and interclass sample pairs can be highly imbalanced in many applications, and this can lead to deteriorating or unsatisfactory performances. The area under the receiver operating characteristic curve (AUC) is a more meaningful performance measure for the imbalanced distribution problem. To tackle the problem as well as to make samples from different modalities directly comparable, a CML method is presented by directly maximizing AUC. The method can be further extended to focus on optimizing partial AUC (pAUC), which is the AUC between two specific false positive rates (FPRs). This is particularly useful in certain applications where only the performances assessed within predefined false positive ranges are critical. The proposed method is formulated as a log-determinant regularized semidefinite optimization problem. For efficient optimization, a minibatch proximal point algorithm is developed. The algorithm is experimentally verified stable with the size of sampled pairs that form a minibatch at each iteration. Several data sets have been used in evaluation, including three cross-modal data sets on face recognition under various scenarios and a single modal data set, the Labeled Faces in the Wild. Results demonstrate the effectiveness of the proposed methods and marked improvements over the existing methods. Specifically, pAUC-optimized CML proves to be more competitive for performance measures such as Rank-1 and verification rate at FPR = 0.1%.