We propose a novel method using Bayesian networks to learn the structure of effective connectivity among brain regions involved in a functional MR experiment. The approach is exploratory in the sense that it does not require an a priori model as in the earlier approaches, such as the Structural Equation Modeling or Dynamic Causal Modeling, which can only affirm or refute the connectivity of a previously known anatomical model or a hypothesized model. The conditional probabilities that render the interactions among brain regions in Bayesian networks represent the connectivity in the complete statistical sense. The present method is applicable even when the number of regions involved in the cognitive network is large or unknown. We demonstrate the present approach by using synthetic data and fMRI data collected in silent word reading and counting Stroop tasks.