Computational prediction of drug-target interaction (DTI) is important for the new drug discovery. Currently, the deep neural network (DNN) has been widely used in DTI prediction. However, parameters of the DNN could be insufficiently trained and features of the data could be insufficiently utilized, because the DTI data is limited and its dimension is very high. To deal with the above problems, in this paper, a graph auto-encoder and multi-subspace deep neural network (GAEMSDNN) is designed. GAEMSDNN enhances its learning ability with a graph auto-encoder, a subspace layer and an ensemble layer. The graph auto-encoder can preserve the reconstruction information. The subspace layer can obtain different strong feature subsets. The ensemble layer in the GAEMSDNN can comprehensively utilize these strong feature subsets in a unified optimization framework. As a result, more features can be extracted from the network input and the DNN network can be better trained. In experiments, the results of GAEMSDNN are significantly improved compared to the previous methods, which validates the effectiveness of our strategies.