A transmission for a vehicle includes a transmission shift unit that receives a shift command of the vehicle, a driving unit that generates a driving force for causing the transmission shift unit to be switched between positions, and a controller configured to control the driving unit for causing the transmission shift unit to be switched between the positions depending on whether a preset condition is satisfied. In particular, the driving unit includes a first stator to generate magnetic flux, a first rotor including first inner permanent magnets and second inner permanent magnets and configured to be rotated by the magnetic flux transmitted to the first inner permanent magnets, outer permanent magnets, a second rotor disposed between the second inner permanent magnets and the outer permanent magnets, and a clutch unit disposed between the first rotor and the second rotor.