Antifreeze proteins (AFPs), which are present in the bodily fluids of organisms inhabiting cold environments, function as inhibitors of ice growth by binding to certain planes of ice crystals. However, the exact mechanism of ice growth inhibition is still poorly understood as it is exceedingly difficult to experimentally analyze the molecular-scale growth kinetics of ice crystals at the planes to which the proteins bind. This review paper focuses on computer simulation studies on the mechanism of ice growth inhibition by AFPs. Recent molecular dynamics simulations of a growing ice-water interface to which protein is bound have indicated that, when the protein is stably bound to the interface, the growth rate of ice surrounding the protein decreases drastically, owing to depression of the ice melting point through the Gibbs-Thomson effect. The observed decrease in growth rate is expected to correspond to ice growth inhibition in real-world systems. In addition to presenting published simulation studies on the mechanism of ice growth inhibition by AFPs, this review also outlines the direction of future simulation studies in this field.