Recently, the convolutional neural network (CNN)-based hashing method has achieved its promising performance for image retrieval. However, tackling the discrepancy between quantization error minimization and discriminability maximization of the network outputs simultaneously still remains unsolved. Distinguished from the previous works, which only can search an equilibrium point within the discrepancy, we propose a novel deep supervised hashing based on stable distribution (DSHSD) to eliminate the discrepancy with distribution consistency guarantee. First, we utilize a smooth projection function, in which the amount of smoothing is adaptable, to relax the discrete constraint instead of any quantization regularizer. Second, a mathematical connection between the smooth projection and the feature distribution is made to maintain distribution consistency. A relaxed multi-semantic information fusion method is implemented to make hash codes learned to preserve more semantic information and accelerate the training convergence. According to stable distribution, we propose a novel hashing framework to eliminate the discrepancy and support fast image retrieval. The extensive experiments on the CIFAR-10, NUS-WIDE, and ImageNet datasets show that our method can outperform the state-of-the-art methods from various perspectives.