The precision of path tracking is fundamental for the safe autonomous operation of intelligent vehicles. In order to address the vibration issue in sliding mode control systems and enhance the control precision of the path tracking controller, a novel Integral Sliding Mode Control strategy with Activation Function (PIDSM-AF) is proposed. Firstly, based on the two-degree-of-freedom vehicle model, the dynamic model of the vehicle is decomposed into a lateral error model to establish the lateral control model. Then, employing the extremum method, an integral sliding mode surface incorporating both heading angle error and lateral error is constructed. Considering the difficulty of eliminating system vibrations with general exponential convergence rates, this study introduces a nonlinear activation function based on the improved exponential convergence rate and designs a lateral path tracking controller based on the activation function sliding mode control. Finally, the improved sliding mode controller is subjected to double lane-change tests through Carsim-Simulink co-simulation. The results indicate that compared to the traditional terminal sliding mode controller, the tracking accuracy of the optimized integral sliding mode controller is improved by approximately 64% and 34.9% in maximum lateral position deviation under low-speed low-adhesion and high-speed high-adhesion conditions respectively, and the average lateral position deviation is improved by approximately 68.4% and 59.7%. Moreover, the optimized controller effectively suppresses the oscillations and overshoot variations of the vehicle"s heading angle and front wheel angle, demonstrating strong robustness.