In this work, we propose an approach that features deep feature embedding learning and hierarchical classification with triplet loss function for Acoustic Scene Classification (ASC). In the one hand, a deep convolutional neural network is firstly trained to learn a feature embedding from scene audio signals. Via the trained convolutional neural network, the learned embedding embeds an input into the embedding feature space and transforms it into a high-level feature vector for representation. In the other hand, in order to exploit the structure of the scene categories, the original scene classification problem is structured into a hierarchy where similar categories are grouped into meta-categories. Then, hierarchical classification is accomplished using deep neural network classifiers associated with triplet loss function. Our experiments show that the proposed system achieves good performance on both the DCASE 2018 Task 1A and 1B datasets, resulting in accuracy gains of 15.6% and 16.6% absolute over the DCASE 2018 baseline on Task 1A and 1B, respectively.