In warehouses with vast quantities of heavy goods, heavy-duty forklift Automated Guided Vehicles (AGVs) play a key role in facilitating efficient warehouse automation. Due to their large load capacity and high inertia, heavy-duty forklift AGVs struggle to automatically navigate optimized routes. Additionally, rapid acceleration and deceleration can pose safety hazards. This paper proposes a velocity-adaptive model predictive control (MPC)-based path tracking method for heavy-duty forklift AGVs. The movement of heavy-duty forklift-type AGVs is categorized into straight-line and curve-turning motions, corresponding to the straight and curved sections of the reference path, respectively. These sections are segmented based on their curvature. The best driving speeds for straight and curved sections were 1.5 m/s and 0.3 m/s, respectively, while the optimal acceleration rates were 0.2 m/s² for acceleration and −0.2 m/s² for deceleration in straight paths and 0.3 m/s² for acceleration with −0.15 m/s² for deceleration in curves. Moreover, preferred sampling times, prediction domain, and control domain were determined through simulations at various speeds. Four path tracking methods, including pure tracking, Linear Quadratic Regulator (LQR), MPC, and the velocity-adaptive MPC, were simulated and evaluated under straight-line, turning, and complex double lane change conditions. Field experiments conducted in a warehouse environment demonstrated the effectiveness of the proposed path tracking method. Findings have implications for advancing path tracking control in narrow aisles.