Accent classification or AC is a task to predict the accent type of an input utterance, and it can be used as a preliminary step toward accented speech recognition and accent conversion. Existing studies have often achieved such classification by training a neural network model to minimize the classification error of the predicted accent label, which can be obtained as a model output. Since we optimize the entire model only from the perspective of classification loss during training time in this approach, the model might learn to predict the accent type from irrelevant features, such as individual speaker identity, which are not informative during test time. To address this problem, we propose a GE2E-AC, in which we train a model to extract accent embedding or AE of an input utterance such that the AEs of the same accent class get closer, instead of directly minimizing the classification loss. We experimentally show the effectiveness of the proposed GE2E-AC, compared to the baseline model trained with the conventional cross-entropy-based loss.