The great amount of gene expression data has brought a big challenge for the discovery of Gene Regulatory Network (GRN). For network reconstruction and the investigation of regulatory relations, it is desirable to ensure directness of links between genes on a map, infer their directionality and explore candidate biological functions from high-throughput transcriptomic data. To address these problems, we introduce a Boolean Function Network (BFN) model based on techniques of hidden Markov model (HMM), likelihood ratio test and Boolean logic functions. BFN consists of two consecutive tests to establish links between pairs of genes and check their directness. We evaluate the performance of BFN through the application to S. cerevisiae time course data. BFN produces regulatory relations which show consistency with succession of cell cycle phases. Furthermore, it also improves sensitivity and specificity when compared with alternative methods of genetic network reverse engineering. Moreover, we demonstrate that BFN can provide proper resolution for GO enrichment of gene sets. Finally, the Boolean functions discovered by BFN can provide useful insights for the identification of control mechanisms of regulatory processes, which is the special advantage of the proposed approach. In combination with low computational complexity, BFN can serve as an efficient screening tool to reconstruct genes relations on the whole genome level. In addition, the BFN approach is also feasible to a wide range of time course datasets.