It has been reported that the communication cost for synchronizing gradients can be a bottleneck, which limits the scalability of distributed deep learning. Using low-precision gradients is a promising technique for reducing the bandwidth requirement. In this work, we propose Auto Precision Scaling (APS), an algorithm that can improve the accuracy when we communicate gradients by low-precision floating-point values. APS can improve the accuracy for all precisions with a trivial communication cost. Our experimental results show that for many applications, APS can train state-of-the-art models by 8-bit gradients with no or only a tiny accuracy loss (<0.05%). Furthermore, we can avoid any accuracy loss by designing a hybrid-precision technique. Finally, we propose a performance model to evaluate the proposed method. Our experimental results show that APS can get a significant speedup over state-of-the-art methods. To make it available to researchers and developers, we design and implement CPD (Customized-Precision Deep Learning) system, which can simulate the training process using an arbitrary low-precision customized floating-point format. We integrate CPD into PyTorch and make it open-source.