Graph Neural Networks (GNNs) have received significant attention due to their state-of-the-art performance on various graph representation learning tasks. However, recent studies reveal that GNNs are vulnerable to adversarial attacks, i.e. an attacker is able to fool the GNNs by perturbing the graph structure or node features deliberately. While being able to successfully decrease the performance of GNNs, most existing attacking algorithms require access to either the model parameters or the training data, which is not practical in the real world. In this paper, we develop deeper insights into the Mettack algorithm, which is a representative grey-box attacking method, and then we propose a gradient-based black-box attacking algorithm. Firstly, we show that the Mettack algorithm will perturb the edges unevenly, thus the attack will be highly dependent on a specific training set. As a result, a simple yet useful strategy to defense against Mettack is to train the GNN with the validation set. Secondly, to overcome the drawbacks, we propose the Black-Box Gradient Attack (BBGA) algorithm. Extensive experiments demonstrate that out proposed method is able to achieve stable attack performance without accessing the training sets of the GNNs. Further results shows that our proposed method is also applicable when attacking against various defense methods.