Recent evidence in cognitive neuroscience has suggested that attention is a complex organ system subserved by at least three attentional networks in the brain, for alerting, orienting, and executive control functions. However, how these different networks work together to give rise to the seemingly unitary mental faculty of attention remains unclear. We describe a connectionist model of human attentional networks to explore the possible interplays among the networks from a computational perspective. This model is developed in the framework of leabra (local, error-driven, and associative, biologically realistic algorithm) and simultaneously involves these attentional networks connected in a biologically inspired way. We evaluate the model by simulating the empirical data collected on normal human subjects using the Attentional Network Test (ANT). The simulation results fit the experimental data well. In addition, we show that the same model, with a single parameter change that affects executive control, is able to simulate the empirical data collected from patients with schizophrenia. This model represents a plausible connectionist explanation for the functional structure and interaction of human attentional networks.