The random access protocol is a critical technique widely used in various wireless networks. A significant challenge is analyzing the stability of the random access system when a large number of users transmit packets independently. Although the congestion control policy can enhance the stability of the system, there is currently a lack of quantitative analysis on the stability of random access with congestion control. In this paper, we analyze the random access system with congestion control and quantify its stability. Specifically, we consider a congestion control scheme to enhance the stability of the random access system and present the graphical analytical model. Based on this graphical model, we qualitatively discuss the behavioral variations of the system as it works and quantify its stability.