Graph neural networks (GNNs) have found successful applications in various graph-related tasks. However, recent studies have shown that many GNNs are vulnerable to adversarial attacks. In a vast majority of existing studies, adversarial attacks on GNNs are launched via direct modification of the original graph such as adding/removing links, which may not be applicable in practice. In this paper, we focus on a realistic attack operation via injecting fake nodes. The proposed Global Attack strategy via Node Injection (GANI) is designed under the comprehensive consideration of an unnoticeable perturbation setting from both structure and feature domains. Specifically, to make the node injections as imperceptible and effective as possible, we propose a sampling operation to determine the degree of the newly injected nodes, and then generate features and select neighbors for these injected nodes based on the statistical information of features and evolutionary perturbations obtained from a genetic algorithm, respectively. In particular, the proposed feature generation mechanism is suitable for both binary and continuous node features. Extensive experimental results on benchmark datasets against both general and defended GNNs show strong attack performance of GANI. Moreover, the imperceptibility analyses also demonstrate that GANI achieves a relatively unnoticeable injection on benchmark datasets.