In the realm of System Biology, it is a challenging endeavor to infer a gene regulatory network from time-series gene expression data. Numerous Boolean network inference techniques have emerged for reconstructing a gene regulatory network from a time series gene expression dataset. However, most of these techniques pose scalability concerns given their capability to consider only 2 to 3 regulatory genes over a specific target gene. To overcome this limitation, a novel inference method, LBF- MI, has been proposed in this research. This two-phase method utilizes limited Boolean functions and multivariate mutual information to reconstruct a Boolean gene regulatory network from time-series gene expression data. Initially, Boolean functions are applied to determine the optimum solutions. In case of failure, multivariate mutual information is applied to obtain the optimum solutions. This research conducted a performance-comparison experiment between LBF-MI and two other methods: Context Likelihood Relatedness, and Relevance Network. When examined on artificial as well as real time-series gene expression data, the outcomes exhibited that the proposed LBF-MI method outperformed Context Likelihood Relatedness and Relevance Network on artificial datasets, and two real Escherichia Coli datasets (E. coli gene regulatory network, and SOS response of E. coli regulatory network).