A transmission for a vehicle may include a first input shaft continuously receiving rotational power from a power source; a second input shaft selectively receiving the rotational power of the power source through a clutch; a first counter shaft and a second counter shaft connected to the first input shaft and the second input shaft through a transfer gear pair, respectively; a controlling device selecting the transfer gear pair to transfer the rotational power from the first input shaft and the second input shaft to the first counter shaft and the second counter shaft; a one-way clutch allowing the rotational power provided to the first input shaft to be transferred only from the first input shaft toward the first counter shaft.