This paper addresses the feedback stabilization problem for a gantry crane system with input constraints. Such a system is described by a wave equation interconnected at the boundary conditions with a double integrator, which represents the top cart's position and its speed. We propose a simple nested-saturation proportional derivative feedback which ensures that the control inputs remain within certain given limits. Global asymptotic stability of the origin of the closed-loop system is established. To this end, a new weak Lyapunov functional and a new methodology to study pre-compactness of solutions are introduced. Numerical simulations are presented to illustrate the effectiveness of the proposed control method.