The deeply hierarchical structures enable deep neural networks (DNNs) to fit extremely complex target functions. However, the complex interaction between layers also makes the learning process of a particular layer poorly understood. This work demonstrates that the shallower layers of DNNs tend to converge faster than the deeper layers. We call this phenomenon Layer Convergence Bias. We also uncover the fundamental reason behind this phenomenon: Flatter local minima of shallower layers make their gradients more stable and predictive, allowing for faster training. Another surprising result is that the shallower layers tend to learn the low-frequency components of the target function, while the deeper layers usually learn the high-frequency components. It is consistent with the recent discovery that DNNs learn lower frequency objects faster.