A vehicle transmission system may include an engine outputting power from fuel combustion, a transmission coupled to the engine and including at least one clutch to control torque input from the engine, an supercharger compressing an intake air and supplying the compressed intake air to the engine, and a control unit, where, when a predetermined acceleration condition is satisfied, the control unit is configured to operate the supercharger and to control the transmission according to a transmission clutch stroke operation map corresponding to the operation of the electric supercharger, to vary an engagement speed of the clutch when the supercharger is operated.