Cranes remain a vital tool for the construction of infrastructure such as buildings, bridges, etc. Recently, there has been renewed interest in crane automation in dealing with concerns on safety and possible performance degradation due to system uncertainties and disturbances. One potential solution to the problem is the use of robust techniques based on the Sliding Mode Control (SMC) methodology. Much research has been conducted to design controllers based on linear sliding surfaces, aiming at achieving the desired control performance in finite time. In this context, this paper proposes a control method, based on the Fast Terminal Sliding Mode (FTSM), to guarantee finite-time stability of the crane. To do that, we have derived a mathematical model of the crane using Lagrangian formulation with uncertainties as bounding functions. Then, sliding surfaces based on the hierarchical sliding mode are defined, and a control law is derived using the Lyapunov stability theory. The hierarchical sliding surfaces consist of two layers. The first layer include sliding functions based on FTSM to enable faster convergence of the system to equilibrium. This can have advantages in high precision tracking applications. In the second-layer, the sliding surface is designed from the linear combination of the first layer sliding functions. Also, we have given a proof of the stability of the system in finite time. Extensive simulation results show the proposed controller based on FTSM can achieve higher performance in stabilizing the swinging load of a gantry crane. Laboratorial experiments have been conducted to verify the obtained results in terms of the superior convergence time and improved performance over conventional SMC.