The deep convolutional neural network has strong representative ability, which can learn latent information repeatedly from signal samples and improve the accuracy of automatic modulation classification (AMC). In this paper, a novel compressive convolutional neural network (CCNN) is proposed for AMC, where different constellation images, i.e., regular constellation images (RCs) and contrast enhanced grid constellation images (CGCs), are generated as network inputs from received signals. Moreover, a compressive loss constraint is proposed to train the CCNN, which aims at capturing high-dimensional features for modulation classification. Additionally, CCNN utilizes intra-class compactness and inter-class separability to enhance the classification and robustness performance for the different orders of modulations. The simulation results demonstrate that CCNN displays superior classification and robustness performance than existing AMC methods.