The problem of uncovering transcriptional regulation by transcription factors (TFs) based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM) coupled with its ICM solution is proposed. BSCRFM models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF regulated genes and it admits prior knowledge from existing database regarding TF regulated target genes. An efficient Iterated Conditional Modes (ICM) algorithm is developed, and a maximum a posterior (MAP) solution is calculated from multiple ICM results to avoid the local maximum problem, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can then be obtained. The proposed model's ICM algorithm and MAP solution are evaluated on the simulated systems and results demonstrated the validity and effectiveness of the proposed approach. The proposed model is also applied to the breast cancer microarray data and a TF regulated network is obtained.