The reconstruction of gene regulatory networks based on gene expression data can effectively uncover regulatory relationships between genes and provide a deeper understanding of biological control processes. Non-linear dependence is a common problem in the regulatory mechanisms of gene regulatory networks. Various methods based on information theory have been developed to infer networks. However, the methods have introduced many redundant regulatory relationships in the network inference process. A recent measurement method called distance correlation has, in many cases, shown strong and computationally efficient non-linear correlations. In this paper, we propose a novel regulatory network inference method called the distance-correlation and network topology centrality network (DCNTC) method. The method is based on and extends the Local Density Measurement of Network Node Centrality (LDCNET) algorithm, which has the same choice of network centrality ranking as the LDCNET algorithm, but uses a simpler and more efficient distance correlation measure of association between genes. In this work, we integrate distance correlation and network topological centrality into the reasoning about the structure of gene regulatory networks. We will select optimal thresholds based on the characteristics of the distribution of each gene pair in relation to distance correlation. Experiments were carried out on four network datasets and their performance was compared.