Whereas numerous motor control theories describe the control of arm trajectory during reach, the control of stabilization in a constant arm position (i.e., visuomotor control of arm posture) is less clear. Three potential mechanisms have been proposed for visuomotor control of arm posture: 1) increased impedance of the arm through co-contraction of antagonistic muscles, 2) corrective muscle activity via spinal/supraspinal reflex circuits, and/or 3) intermittent voluntary corrections to errors in position. We examined the cortical mechanisms of visuomotor control of arm posture and tested the hypothesis that cortical error networks contribute to arm stabilization. We collected electroencephalography (EEG) data from 10 young healthy participants across four experimental planar movement tasks. We examined brain activity associated with intermittent voluntary corrections of position error and antagonist co-contraction during stabilization. EEG beta-band (13–26 Hz) power fluctuations were used as indicators of brain activity, and coherence between EEG electrodes was used as a measure of functional connectivity between brain regions. Cortical activity in the sensory, motor, and visual areas during arm stabilization was similar to activity during volitional arm movements and was larger than activity during co-contraction of the arm. However, cortical connectivity between the sensorimotor and visual regions was higher during arm stabilization compared with volitional arm movements and co-contraction of the arm. The difference in cortical activity and connectivity between tasks might be attributed to an underlying visuomotor error network used to update motor commands for visuomotor control of arm posture.