The present study examined directional connections in the brain among resting-state networks (RSNs) when the participant had their eyes open (E0) or had their eyes closed (EC). The resting state fMRI data were collected from 20 healthy participants (9 males, 20.17 +/- 2.74 years) under the EO and EC states. Independent component analysis (ICA) was applied to identify the separated RSNs (i.e., the primary/high-level visual, primary sensory-motor, ventral motor, salience/dorsal attention, and anterior/posterior default-mode networks), and the Gaussian Bayesian network (BN) learning approach was then used to explore the conditional dependencies among these RSNs. The network-to-network directional connections related to EO and EC were depicted, and a support vector machine (SVM) was further employed to identify the directional connection patterns that could effectively discriminate between the two states. The results indicated that the connections among RSNs are directionally connected within a BN during the EO and EC states. The directional connections from the salience network (SN) to the anterior/posterior default-mode networks and the high-level to primary-level visual network were the obvious characteristics of both the EO and EC resting-state BNs. Of the directional connections in BN, the directional connections of the salience and dorsal attention network (DAN) were observed to be discriminative between the EO and EC states. In particular, we noted that the properties of the salience and DANs were in opposite directions. Overall, the present study described the directional connections of RSNs using a BN learning approach during the E0 and EC states, and the results suggested that the directionality of the attention systems (i.e., mainly for the salience and the DAN) in resting state might have Important roles in switching between the EO and EC conditions.