An important problem in systems biology is to reconstruct gene regulatory networks (GRNs) from experimental data and other a priori information. The DREAM project offers some types of experimental data, such as knockout data, knockdown data, time series data, etc. Among them, multifactorial perturbation data are easier and less expensive to obtain than other types of experimental data and are thus more common in practice. In this article, a new algorithm is presented for the inference of GRNs using the DREAM4 multifactorial perturbation data. The GRN inference problem among [Formula: see text] genes is decomposed into [Formula: see text] different regression problems. In each of the regression problems, the expression level of a target gene is predicted solely from the expression level of a potential regulation gene. For different potential regulation genes, different weights for a specific target gene are constructed by using the sum of squared residuals and the Pearson correlation coefficient. Then these weights are normalized to reflect effort differences of regulating distinct genes. By appropriately choosing the parameters of the power law, we constructe a 0-1 integer programming problem. By solving this problem, direct regulation genes for an arbitrary gene can be estimated. And, the normalized weight of a gene is modified, on the basis of the estimation results about the existence of direct regulations to it. These normalized and modified weights are used in queuing the possibility of the existence of a corresponding direct regulation. Computation results with the DREAM4 In Silico Size 100 Multifactorial subchallenge show that estimation performances of the suggested algorithm can even outperform the best team. Using the real data provided by the DREAM5 Network Inference Challenge, estimation performances can be ranked third. Furthermore, the high precision of the obtained most reliable predictions shows the suggested algorithm may be helpful in guiding biological experiment designs.