Visual curve completion is a fundamental problem in understanding the principles of the human visual system. This problem is usually divided into two problems: a grouping problem and a shape problem. On one hand, though perception of the visually completed curve is clearly a global task (for example, a human perceives the Kanizsa triangle only when seeing all three black objects), conventional methods for solving the grouping problem are generally based on local Gestalt laws. On the other hand, the shape of the visually completed curve is usually recovered by minimizing shape energy in existing methods. However, not only do these methods lack mechanisms to adjust the shape of the recovered visual curve using perceptual, psychophysical, and neurophysiological knowledge, but it is also difficult to calculate an explicit representation of the visually completed curve. In this paper, we present a systematic computational model for generating a visually completed curve. Firstly, based on recent studies of perception, psychophysics, and neurophysiology, we formulate a grouping procedure based on the human visual system by seeking a minimum Hamiltonian cycle in a graph, solving the grouping problem in a global manner. Secondly, we employ a B′ezier curve-based model to represent the visually completed curve. Not only is an explicit representation deduced, but we also present a means to integrate knowledge from related areas, such as perception, psychophysics, and neurophysiology, and so on. The proposed computational model has been validated using many modal and amodal completion examples, and desirable results were obtained.