Graph attention network (GAT) is a promising framework to perform aggregation and massage passing on graphs. GATs attention layer extracts the attention coefficients mainly using node features of the current node. But, we believe that attention can be obtained directly from the structural information of the graph. We argue that local graph structures play a dominant role for calculating good attention coefficients and propose a structure-based graph attention layer called local neighborhood graph attention layer (LNGAL). Different from GAT, LNGAL obtains attention only by local graph structural information and abandons the dependence on the features of nodes, which calculates the attention coefficients directly from theoretical formulas, instead of training with labeled data. In LNGAL, the first-order neighborhood of the current node provides a primary contribution to the calculation of attention coefficients, while the second-order neighborhood plays a fine-tune role. Furthermore, we introduce the proposed LNGAL to a multi-scale architecture and design a novel network called local neighborhood graph attention network (LNGAT). In the experimental section, we show that LNGAT network outperforms several recently proposed graph convolutional network-like models and achieves state-of-the-art performance on six open graph datasets.