As the network expands, the exact algorithm of closeness centrality has low efficiency. In this study, a model based on the learning to rank algorithm (RankNet) is proposed to quickly approximate the closeness centrality rank of complex network nodes. Firstly, the study carries out a correlation analysis to obtain important node indicators positively correlated with the closeness centrality and put them as input features of the model. Subsequently, a subset of nodes in a given network is randomly selected and used for the training sample data of the model. The proposed model is verified by a real aviation network dataset and typical complex network models. The experimental results show that the RankNet-based model not only reduces the computational complexity but also keeps a high accuracy of the approximation. In addition, the ranking performance of the proposed model is significantly superior to that of the benchmark model based on regression learning.