The inference of gene regulatory networks (GRNs) from expression data can mine the direct regulations among genes and gain deep insights into biological processes at a network level. During past decades, numerous computational approaches have been introduced for inferring the GRNs. However, many of them still suffer from various problems, e.g., Bayesian network (BN) methods cannot handle large-scale networks due to their high computational complexity, while information theory-based methods cannot identify the directions of regulatory interactions and also suffer from false positive/negative problems. To overcome the limitations, in this work we present a novel algorithm, namely local Bayesian network (LBN), to infer GRNs from gene expression data by using the network decomposition strategy and false-positive edge elimination scheme. Specifically, LBN algorithm first uses conditional mutual information (CMI) to construct an initial network or GRN, which is decomposed into a number of local networks or GRNs. Then, BN method is employed to generate a series of local BNs by selecting the k-nearest neighbors of each gene as its candidate regulatory genes, which significantly reduces the exponential search space from all possible GRN structures. Integrating these local BNs forms a tentative network or GRN by performing CMI, which reduces redundant regulations in the GRN and thus alleviates the false positive problem. The final network or GRN can be obtained by iteratively performing CMI and local BN on the tentative network. In the iterative process, the false or redundant regulations are gradually removed. When tested on the benchmark GRN datasets from DREAM challenge as well as the SOS DNA repair network in E.coli, our results suggest that LBN outperforms other state-of-the-art methods (ARACNE, GENIE3 and NARROMI) significantly, with more accurate and robust performance. In particular, the decomposition strategy with local Bayesian networks not only effectively reduce the computational cost of BN due to much smaller sizes of local GRNs, but also identify the directions of the regulations.