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) is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF regulated genes. The model admits prior knowledge from existing database regarding TF regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the Breast cancer microarray data of patients with Estrogen Receptor positive ER+ status and Estrogen Receptor negative ER- status, respectively.