Existing graph neural networks may suffer from the "suspended animation problem" when the model architecture goes deep. Meanwhile, for some graph learning scenarios, e.g., nodes with text/image attributes or graphs with long-distance node correlations, deep graph neural networks will be necessary for effective graph representation learning. In this paper, we propose a new graph neural network, namely DIFNET (Graph Diffusive Neural Network), for graph representation learning and node classification. DIFNET utilizes both neural gates and graph residual learning for node hidden state modeling, and includes an attention mechanism for node neighborhood information diffusion. Extensive experiments will be done in this paper to compare DIFNET against several state-of-the-art graph neural network models. The experimental results can illustrate both the learning performance advantages and effectiveness of DIFNET, especially in addressing the "suspended animation problem".