Deep hashing methods have achieved great success in multi-label image retrieval due to its computation and storage efficiency. However, most existing methods adopt a relaxation-and-quantization optimization strategy, which inevitably degrades the performance. Besides, existing discrete hashing methods are very time-consuming because of the bit-wise learning strategy. To tackle these issues, we propose a novel deep asymmetric discrete hashing method, called Fast and Multilevel semantic-preserving Discrete Hashing (FMDH). FMDH makes the best of supervised information to preserve the multilevel semantic similarities between multi-label images, and further accelerates the training process. Extensive experiments on two widely used multi-label image datasets demonstrate that FMDH can achieve the state-of-the-art performance on both accuracy and training time efficiency.