The mean firing rate of a border-ownership selective (BOS) neuron encodes where a foreground figure relative to its classical receptive field. Physiological experiments have demonstrated that top-down attention increases firing rates and decreases spike synchrony between them. To elucidate mechanisms of attentional modulation on rates and synchrony of BOS neurons, we developed a spiking neuron network model: BOS neurons receive synaptic input which reflects visual input. The synaptic input strength is modulated multiplicatively by the activity of Grouping neurons whose activity represents the object’s location and mediates top-down attentional projection to BOS neurons. Model simulations agree with experimental findings, showing that attention to an object increases the firing rates of BOS neurons representing it while decreasing spike synchrony between pairs of such neurons. Our results suggest that top-down attention multiplicatively emphasizes synaptic current due to bottom-up visual inputs.