An implementation of attentional bias is presented for a network model that couples excitatory and inhibitory oscillatory units in a manner that is inspired by the mechanisms that generate cortical gamma oscillations. Attentional biases are implemented as oscillatory coherences between excitatory units that encode the spatial location or features of the target and the pool of inhibitory units. This form of attentional bias is motivated by neurophysiological findings that relate selective attention to spike field coherence. Including also pattern recognition mechanisms, we demonstrate how this implementation of attentional bias leads to selection of an attentional target while suppressing distracters for cases of spatial and feature-based attention. With respect to neurophysiological observations, we argue that the recently found positive correlation between high firing rates and strong gamma locking with attention (Vinck, Womelsdorf, Buffalo, Desimone, & Fries, 2013 ) may point to an essential mechanism of the brain’s attentional selection and suppression processes.