The acoustoelectric current in graphene has been investigated as a function of temperature, surface acoustic wave (SAW) intensity, and frequency. At high SAW frequencies, the measured acoustoelectric current decreases with decreasing temperature, but remains positive, which corresponds to the transport of holes, over the whole temperature range studied. The current also exhibits a linear dependence on the SAW intensity, consistent with the interaction between the carriers and SAWs being described by a relatively simple classical relaxation model. At low temperatures and SAW frequencies, the measured acoustoelectric current no longer exhibits a simple linear dependence on the SAW intensity, and the direction of the acoustoelectric current is also observed to reverse under certain experimental conditions.