Due to the success of Graph Neural Networks(GNNs) in graph-structure data, many efforts have been devoted to enhancing the propagation ability and alleviating the over-smoothing problem of GNNs. However, from the perspective of closeness extent of node representations, most existing GNNs pay less attention to the attributes of node representation space. In light of this, we design a Layer Sniffer module that can combine the effects of the local node-level representation closeness extent and the global layer-level information attention. On this basis, we propose a simple Layer Sniffer Graph Neural Network (LSGNN) with a propagation scheme that can fuse neighborhood information of different receptive fields densely and adaptively. Our extensive experiments on three public node classification datasets demonstrate the superior performance and stability of our proposed model.