Graph neural networks (GNNs) are powerful models for many graph-structured tasks. Existing models often assume that a complete structure of a graph is available during training, however, in practice, graph-structured data is usually formed in a streaming fashion, so that learning a graph continuously is often necessary. In this paper, we aim to bridge GNN to lifelong learning by converting a graph problem to a regular learning problem, so that GNN is able to inherit the lifelong learning techniques developed for convolutional neural networks (CNNs). To this end, we propose a new graph topology based on feature cross-correlation, called the feature graph. It takes features as new nodes and turns nodes into independent graphs. This successfully converts the original problem of node classification to graph classification, in which the increasing nodes are turned into independent training samples. In the experiments, we demonstrate the efficiency and effectiveness of feature graph networks (FGN) by continuously learning a sequence of classical graph datasets. We also show that FGN achieves superior performance in human action recognition with distributed streaming signals for wearable devices.