Here we investigate how the extent of spatial attention affects center-surround interaction in visual motion processing. To do so, we measured motion direction discrimination thresholds in humans using drifting gratings and two attention conditions. Participants were instructed to limit their attention to the central part of the stimulus under the narrow attention condition, and to both central and surround parts under the wide attention condition. We found stronger surround suppression under the wide attention condition. The magnitude of the attention effect increased with the size of the surround when the stimulus had low contrast, but did not change when it had high contrast. Results also showed that attention had a weaker effect when the center and surround gratings drifted in opposite directions. Next, to establish a link between the behavioral results and the neuronal response characteristics, we performed computer simulations using the divisive normalization model. Our simulations showed that using smaller versus larger multiplicative attentional gain and parameters derived from the medial temporal (MT) area of the cortex, the model can successfully predict the observed behavioral results. These findings reveal the critical role of spatial attention on surround suppression and establish a link between neuronal activity and behavior. Further, these results also suggest that the reduced surround suppression found in certain clinical disorders (e.g., schizophrenia and autism spectrum disorder) may be caused by abnormal attention mechanisms.