While very deep neural networks have shown effectiveness for computer vision and text classification applications, how to increase the network depth of neural machine translation (NMT) models for better translation quality remains a challenging problem. Directly stacking more blocks to the NMT model results in no improvement and even reduces performance. In this work, we propose an effective two-stage approach with three specially designed components to construct deeper NMT models, which result in significant improvements over the strong Transformer baselines on WMT$14$14 English$\to$→German and English$\to$→French translation tasks\footnote{Our code is available at \url{https://github.com/apeterswu/Depth_Growing_NMT}}.