Modulation classification, recognized as the intermediate step between signal detection and demodulation, is widely deployed in several modern wireless communication systems. Although many approaches have been studied in the last decades for identifying the modulation format of an incoming signal, they often reveal the obstacle of learning radio characteristics for most traditional machine learning algorithms. To overcome this drawback, we propose an accurate modulation classification method by exploiting deep learning for being compatible with constellation diagram. Particularly, a convolutional neural network is developed for proficiently learning the most relevant radio characteristics of gray-scale constellation image. The deep network is specified by multiple processing blocks, where several grouped and asymmetric convolutional layers in each block are organized by a flow-in-flow structure for feature enrichment. These blocks are connected via skip-connection to prevent the vanishing gradient problem while effectively preserving the information identify throughout the network. Regarding several intensive simulations on the constellation image dataset of eight digital modulations, the proposed deep network achieves the remarkable classification accuracy of approximately 87% at 0 dB signal-to-noise ratio (SNR) under a multipath Rayleigh fading channel and further outperforms some state-of-the-art deep models of constellation-based modulation classification.