Most deep supervised cross-modal hashing methods adopt a symmetric strategy to learn hash code， so that the supervision information in large-scale datasets cannot be used effectively. And for the problem of discrete constraints of hash code， relaxation-based strategy is typically adopted， resulting in large quantization error which leads to the sub-optimal hash code. Aiming at the above problems， a Deep Asymmetric Discrete Cross-modal Hashing （DADCH） method was proposed. Firstly， an asymmetric learning framework combining deep neural networks and dictionary learning was proposed to learn the hash code of query instances and database instances， thereby mining the supervision information of the data more effectively and reducing the training time of the model. Then， the discrete optimization algorithm was used to optimize the hash code matrix column by column to reduce the quantization error of the hash code binarization. At the same time， in order to fully mine the semantic information of the data， a label layer was added to the neural network for label prediction， and the semantic information embedding was used to embed discrimination information of different categories into the hash code through linear mapping to make the hash code more discriminative. Experimental results show that on IAPR-TC12， MIRFLICKR-25K and NUS-WIDE datasets， the mean Average Precision （mAP） of the proposed method on retrieval text by image is about 11.6， 5.2 and 14.7 percentage points higher than that of the advanced deep cross-modal retrieval method — Self-Supervised Adversarial Hashing （SSAH） proposed in recent years respectively.