A driving system for an electric vehicle may include a shift assembly receiving power from a motor, and providing a plurality of shift gears using a plurality of meshed external gear pairs, a clutch intermittently transferring power from the motor to the shift assembly, a gear lever allowing a driver to sequentially select a plurality of assigned positions that are discontinuously disposed, a position sensor detecting the assigned positions to which the gear lever sequentially moves, on the basis of continuous changes in physical quantities, a clutch actuator actuating the clutch, a shift actuator actuating the shift assembly to change gear shifts, and a controller configured for controlling the clutch actuator, the shift actuator, and the motor to change gear shifts by receiving signals from the position sensor.