Deep learning (DL) nowadays activates the advancement of multiple research fields, from signal processing to computer vision and communication. Compared with traditional machine learning (ML) algorithms, some DL architectures such as convolutional neural network (CNN) allow learning feature automatically without expert knowledge in a specific domain. Inspired by the notable achievement of DL for general image classification, this work studies an efficient CNN-based approach for automatic modulation classification which is recognized as the fundamental task in several modern communication systems. Besides the architecture organized by several blocks of parallel asymmetric convolutional layers, the proposed network is specialized by two mechanisms: skip-connection for the prevention of vanishing gradient and reusable-feature depth-concatenation for an optimal feature utilization via accumulating the deep feature at multi-scale representation. According performance evaluation, our method gains the 24-modulation classification rate of 85.10% at +10 dB SNR on the most challenging and large-scale DeepSig: RadioML (version 2018.01A) dataset.