A driving system is provided for a vehicle that includes an engine, a driving motor connected to the engine and generating a driving force, and a transmission that receives a driving force generated from the driving motor and changes a direction of the driving force. Additionally, a clutch selectively connects between the driving motor and the transmission and a controller operates the driving motor and the transmission. The controller determines whether a direction inversion shifting condition is satisfied and performs a direction inversion shifting using the driving motor when the direction inversion shifting condition is satisfied.