This paper presents the velocity control system design for overhead crane gantry drives, which allows the suppression of elastic horizontal vibrations of its structure. During the design process an assumption is made that the plant can be approximated with sufficient accuracy via the three-mass mechanical system, its parameters being calculated so that the transient responses would match the simulation results of the finite-element model from Comsol Multiphysics software. A dual-channel velocity cascade control system with additional feedbacks of velocity differences between gantry wheels and trolley was designed to suppress the elastic structure vibrations. The efficiency of presented approach was verified via finite-element software simulation. The acquired results indicate that it is possible to achieve efficient vibrations cancellation of an overhead crane structure by means of electric drive.