Variable air volume air-conditioning system (VAV system) has multiple control loops that interfered with each other, which has serious impacts on its actual operation effect. To solve this problem, the index of global hydraulic stability, which takes the physical quantity of the pipe network pressure and the air flow rate as reference, is proposed based on Graph theory, and a pipe network model for the hydraulic calculation is built. Then, the simulation study based on the actual operation data is carried out in MATLAB. The distribution of the pressure and the air flow in the pipe network is obtained, and the action interferences among adjacent terminal boxes are analyzed based on global hydraulic stability under damper position regulation strategy (DP strategy) and fan frequency regulation strategy (FF strategy). Results indicate that the FF strategy can decrease the total change distance of the damper position compared with the DP strategy, and then the fluctuation of the pressure and the air flow can be reduced. The contribution of this study is to provide an evaluation index of global hydraulic stability, which can also be used in other air-conditioning systems with multiple terminals and multiple control loops.