Model compression methods have become popular in recent years, which aim to alleviate the heavy load of deep neural networks (DNNs) in real-world applications. However, most of the existing compression methods have two limitations: 1) they usually adopt a cumbersome process, including pertaining, training with a sparsity constraint, pruning/decomposition, and fine-tuning. Moreover, the last three stages are usually iterated multiple times. 2) The models are pretrained under explicit sparsity or low-rank assumptions, which are difficult to guarantee wide appropriateness. In this article, we propose an efficient decomposition and pruning (EDP) scheme via constructing a compressed-aware block that can automatically minimize the rank of the weight matrix and identify the redundant channels. Specifically, we embed the compressed-aware block by decomposing one network layer into two layers: a new weight matrix layer and a coefficient matrix layer. By imposing regularizers on the coefficient matrix, the new weight matrix learns to become a low-rank basis weight, and its corresponding channels become sparse. In this way, the proposed compressedaware block simultaneously achieves low-rank decomposition and channel pruning by only one single data-driven training stage. Moreover, the network of architecture is further compressed and optimized by a novel Pruning & Merging (PM) module which prunes redundant channels and merges redundant decomposed layers. Experimental results (17 competitors) on different data sets and networks demonstrate that the proposed EDP achieves a high compression ratio with acceptable accuracy degradation and outperforms state-of-the-arts on compression rate, accuracy, inference time, and run-time memory.