Graph neural networks (GNNs) have achieved outstanding performance in learning graph-structured data and various tasks. However, many current GNNs suffer from three common problems when facing large-size graphs or using a deeper structure: neighbors explosion, node dependence, and oversmoothing. Such problems attribute to the data structures of the graph itself or the designing of the multi-layers GNNs framework, and can lead to low training efficiency and high space complexity. To deal with these problems, in this paper, we propose a general subgraph-based training framework, namely Ripple Walk Training (RWT), for deep and large graph neural networks. RWT samples subgraphs from the full graph to constitute a mini-batch, and the full GNN is updated based on the mini-batch gradient. We analyze the high-quality subgraphs to train GNNs in a theoretical way. A novel sampling method Ripple Walk Sampler works for sampling these high-quality subgraphs to constitute the mini-batch, which considers both the randomness and connectivity of the graph-structured data. Extensive experiments on different sizes of graphs demonstrate the effectiveness and efficiency of RWT in training various GNNs (GCN & GAT).