As the number of internet users appears to steadily increase each year, Internet Gaming Disorder (IGD) is bound to increase as well. The question how this increase will take place, and what factors have the largest impact on this increase, naturally arises. We consider a system of ordinary differential equations as a simple mathematical model of the population dynamics about the internet gaming. We assume three stages about the internet gamer’s state: moderate, addictive, and under treatment. The transition of the gamer’s state between the moderate and the addictive stages is significantly affected by the social nature of internet gaming. As the activity of social interaction gets higher, the gamer would be more likely to become addictive. With the inherent social reinforcement of internet game, the addictive gamer would hardly recontrol his/herself to recover to the moderate gamer. Our result on the model demonstrates the importance of earlier initiation of a system to check the IGD and lead to some medical/therapeutic treatment. Otherwise, the number of addictive gamers would become larger beyond the socially controllable level.