Graph neural networks (GNNs) have shown convincing performance in learning powerful node representations that preserve both node attributes and graph structural information. However, many GNNs encounter problems in effectiveness and efficiency when they are designed with a deeper network structure or handle large-sized graphs. Several sampling algorithms have been proposed for improving and accelerating the training of GNNs, yet they ignore understanding the source of GNNs performance gain. The measurement of information within graph data can help the sampling algorithms to keep high-value information while removing redundant information and even noise. In this paper, we propose a Metric-Guided (MeGuide) subgraph learning framework for GNNs. MeGuide employs two novel metrics: Feature Smoothness and Connection Failure Distance to guide the subgraph sampling and mini-batch based training. Feature Smoothness is designed for analyzing the feature of nodes to retain the most valuable information, while Connection Failure Distance can measure the structural information to control the size of subgraphs. We demonstrate the effectiveness and efficiency of MeGuide in training various GNNs on multiple data sets.