Recent physiological studies have reported that neurons in the cortical area V4 are selective to curvature along object contour. The neurons are capable of discriminating convexity and concavity, and indicating the direction of the curvature with respect to the contour projected onto their cRF. We propose that surface representation plays a crucial role in constructing the selectivity for curvature because convexity/concavity cannot be determined without the construction of object surface. To test the proposal, we developed a computational-model of V1-V4 networks that computes spatiotemporal activities of single cells, and carried out the simulations with the stimuli used by the physiological studies. The model neurons reproduced the selectivity for specific curvature and direction. Population of the model cells showed a bias toward convex curvature as consistent with V4 population in vivo. These results support that the representation of surface is crucial for the construction of the selectivity in V4.