Graph Neural Networks (GNNs) have drawn considerable attention in recent years and achieved outstanding performance in many tasks. Most empirical studies of GNNs assume that the observed graph represents a complete and accurate picture of node relationship. However, this fundamental assumption cannot always be satisfied, since the real- world graphs from complex systems are error-prone and may not be compatible with the properties of GNNs. Therefore, GNNs solely relying on original graph may cause unsatisfactory results, one typical example of which is that GNNs perform well on graphs with homophily while fail on the disassortative situation. In this paper, we propose graph estimation neural networks GEN, which estimates graph structure for GNNs. Specifically, our GEN presents a structure model to fit the mechanism of GNNs by generating graphs with community structure, and an observation model that injects multifaced observations into calculating the posterior distribution of graphs and is the first to incorporate multi- order neighborhood information. With above two models, the estimation of graph is implemented based on Bayesian inference to maximize the posterior probability, which attains mutual optimization with GNN parameters in an iterative framework. To comprehensively evaluate the performance of GEN, we perform a set of experiments on several benchmark datasets with different homophily and a synthetic dataset, where the experimental results demonstrate the effectiveness of our GEN and rationality of the estimated graph.