This paper analyzes the effect of network neutrality regulation on social welfare using the two-sided market under the network congestion. This paper deals with zero price rule regulation which means the price regulation on the side of content. The results are as follows : First, under the monopoly platform, internet use price, contents price, and the number of internet user and content provider are all decreasing as the network congestion increases. Second, under the monopoly platform internet use price, contents price, and the number of internet user and content provider are all increasing as the network capacity increases. Third, the price of internet use and contents internet use which maximize social welfare are increasing and the number of internet user and content provider are decreasing as the network congestion increases. Fourth, optimal network capacity for monopoly platform provider is less than socially optimal network capacity. Fifth, if network neutrality regulation is enforced, the price of internet use is higher than monopoly platform provider and the price of contents is lower than monopoly platform provider. Also, the number of internet user is less than monopoly platform provider and the number of content provider is more than that. By the way, when network congestion increases, internet use price, the number of internet user, and the number of content provider are decreasing. Sixth, network neutrality regulation is more effective for internet user side than contents provider when network congestion is considered. This means that network neutrality regulation is not effective for contents market side when network congestion is seriously large.