Surface acoustic waves (SAWs) are elastic waves that propagate on the surface of a solid, much like waves on the ocean, with SAW devices used widely in communication and sensing. The ability to dynamically control the properties of SAWs would allow the creation of devices with improved performance or new functionality. However, so far it has proved extremely difficult to develop a practical way of achieving this control. In this paper we demonstrate voltage control of SAWs in a hybrid graphene-lithium niobate device. The velocity shift of the SAWs was measured as the conductivity of the graphene was modulated using an ion-gel gate, with a 0.1% velocity shift achieved for a bias of approximately 1 V. This velocity shift is comparable to that previously achieved in much more complicated hybrid semiconductor devices, and optimization of this approach could therefore lead to a practical, cost-effective voltage-controlled velocity shifter. In addition, the piezoelectric fields associated with the SAW can also be used to trap and transport the charge carriers within the graphene. Uniquely to graphene, we show that the acoustoelectric current in the same device can be reversed, and switched off, using the gate voltage.