In covert visual attention, frontoparietal attention control areas are thought to issue signals to selectively bias sensory neurons to facilitate behaviorally relevant information and suppress distraction. We investigated the relationship between activity in attention control areas and attention-related modulation of posterior alpha activity using simultaneous electroencephalography (EEG) and functional magnetic resonance imaging in humans during cued visual-spatial attention. Correlating single-trial EEG alpha power with blood-oxygen-level dependent (BOLD) activity, we found that BOLD in the intraparietal sulcus (IPS) and left middle frontal gyrus was inversely correlated with occipital alpha power. Importantly, in IPS, inverse correlations were stronger for alpha within the hemisphere contralateral to the attended hemifield, implicating the IPS in the enhancement of task-relevant sensory areas. Positive BOLD-alpha correlations were observed in sensorimotor cortices and the default mode network, suggesting a mechanism of active suppression over task-irrelevant areas. The magnitude of cue-induced alpha lateralization was positively correlated with BOLD in dorsal anterior cingulate cortex and dorsolateral prefrontal cortex, implicating a role of executive control in attention. These results show that IPS and frontal executive areas are the main sources of biasing influences on task-relevant visual cortex, whereas task-irrelevant default mode network and sensorimotor cortex are inhibited during visual attention.