To address the degradation of path tracking performance caused by model inaccuracy due to nonlinear variations in tire lateral forces, an adaptive predictive function control (APFC) algorithm incorporating variable cornering stiffness parameters is proposed. The nonlinear characteristics of tire lateral forces and their influence on cornering stiffness are analyzed. A real-time tire lateral force estimator based on the square-root cubature Kalman filter is established, and an adaptive adjustment strategy is developed to modify tire cornering stiffness according to actual lateral force variations. The proposed strategy is validated through co-simulation in Simulink/CarSim and real vehicle tests. Simulation results show that, compared with model predictive control (MPC), the root mean square (RMS) values of lateral position error are reduced by 19.43% and 31.67% under high/low adhesion double-lane-change conditions, respectively. For high-adhesion large-curvature scenarios, the RMS error is reduced by 37.89%. Real vehicle tests demonstrate that the APFC strategy reduces average computation time by 54.09% and decreases the RMS lateral position error by 38.23% compared with MPC.