During the operation of the automotive drive shaft system, the ball-type universal joint will generate a secondary torque, which will affect the torque transmission of the automotive drive shaft system and the comfort of the automobile. Under the influence of the internal friction of the ball-type universal joint, the secondary torque generates a torque component on the plane where the working angle is located and the plane perpendicular to the working angle. To effectively calculate and analyze the secondary torque, this paper establishes a multi-body dynamic model of the ball-type universal joint. At the same time, the secondary torque of the ball-type universal joint is measured by the NVH multi-function test bench, which verifies the validity of the multi-body dynamic model. In order to improve the analysis efficiency of the secondary torque, a proxy model of the secondary torque of the ball-type universal joint is established based on the multi-body dynamic model. Through the proxy model, the influence of contact angle, conformity value, offset, friction coefficient, and the interference fit between ball and cage window on the secondary torque is analyzed. Using the global sensitivity analysis method of partial derivatives, the sensitivity analysis of the proxy model is carried out, and the degree of influence of each influencing factor on the secondary torque is further determined. According to the results of sensitivity analysis, this article gives measures to optimize the secondary torque.