Superpixels provide an efficient representation of images, and are applicable for subsequent vision tasks. In this paper, we propose an edge-aware superpixel algorithm based on an unsupervised convolutional neural network (CNN). Noticing that to adhere the boundaries of objects is one of the most essential characteristics of superpixels, we propose an entropy-based edge-aware term, which helps fit the differential model of the pixel-superpixel soft-assignment matrix predicted from CNN to image gradients, i.e. generate boundary-aligning superpixels. The proposed algorithm yields more boundary-adhering superpixels, and experimental results on BSDS500 show the effectiveness of the proposed edge-aware term.