Recent physiological studies of alert primates have revealed cortical neural correlates of key steps in a perceptual decision-making process. To elucidate synaptic mechanisms of decision making, I investigated a biophysically realistic cortical network model for a visual discrimination experiment. In the model, slow recurrent excitation and feedback inhibition produce attractor dynamics that amplify the difference between conflicting inputs and generates a binary choice. The model is shown to account for salient characteristics of the observed decision-correlated neural activity, as well as the animal's psychometric function and reaction times. These results suggest that recurrent excitation mediated by NMDA receptors provides a candidate cellular mechanism for the slow time integration of sensory stimuli and the formation of categorical choices in a decision-making neocortical network.