Inferring gene regulatory networks from expression data is a central problem in systems biology. It is critical for identifying complicated regulatory relationships among genes and understanding regulatory mechanisms in cells. Various methods based on information theory have been developed to infer networks. However, the methods introduce many redundant regulatory relationships in the process of network inference owing to noise in the data and the threshold tenability of the method. In this paper, we propose a novel network inference method using redundancy reduction in the minimum-redundancy network (MRNET) algorithm (RRMRNET) to improve regulatory network structure. The method is based on and extends the MRNET algorithm. Two redundancy reduction strategies are given in the method: one is used to obtain a candidate regulator gene set for each target gene by reducing non-regulation and weakly indirect regulation of genes; the other assigns the best-first regulator gene to each target gene to eliminate redundant regulatory relationships caused by noise in the MRNET algorithm. Eventually, the candidate regulator gene set and the best-first regulatory gene for each gene were used in the MRNET to obtain a complete network structure. The proposed method was performed on six network datasets, and its performance was also compared to that of other network inference methods based on information theory. Extensive experimental results demonstrated the effectiveness of the proposed method.