The bi-tandem axial piston pump is an indispensable powerhouse in high-pressure and high-power engineering hydraulic systems, with its output flow response characteristics under pressure disturbance exerting a significant influence on the working process of double pumps. Unfortunately, the stability of the original single-loop mechanical–hydraulic servo control system is sensitive to unpredictable interference. To alleviate this quandary, this paper proposes a dual-loop positive flow control method for the flow control of the bi-tandem axial piston pump, establishes a mathematical model of the bi-tandem axial piston pump with dual-loop positive flow control, and establishes a simulation model based on Simulink. The validity of the model is verified by experiments. The performance advantages of the dual-loop positive flow control method relative to the single-loop positive flow control method are analyzed. The results show a faster response speed and smaller steady-state error with the dual-loop method, which performs better than the original single-loop positive flow control. Furthermore, the study examines the influence of different forms, degrees, and directions of pressure disturbance on the dynamic response characteristics of the bi-tandem axial piston pump. Symmetric pressure disturbance results in an increase in the maximum relative error of the output flow proportional to its degree. Notably, the influence of asymmetric pressure disturbance on the output flow of the double pumps possesses characteristics of a superimposable nature, and the steady-state value of the output flow is highly dependent on superimposed pressure disturbance and less affected by the action time point of asymmetric pressure disturbance. Further, the unloading pressure disturbance exerts less influence on the system compared to the loading pressure disturbance. This paper provides valuable insights into improving the response speed and control accuracy of bi-tandem axial piston pumps equipped with positive flow control.