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 ICM algorithm is developed and a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the ICM algorithm 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 regarding ER status is obtained.