A power transmission apparatus of a hybrid electric vehicle using an engine and a motor/generator as power sources includes: a first input shaft selectively connected to a rotor of the motor/generator; a second input shaft disposed external to the first input shaft, and selectively connected to the rotor; an idle shaft disposed in parallel with the first input shaft; an intermediate shaft shifting rotational power transmitted from the first input shaft to the idle shaft; a first output shaft shifting and outputting rotational power transmitted from the second input shaft and the idle shaft; a second output shaft shifting and outputting rotational power transmitted from the first input shaft; and a plurality of gear sets shifting the rotational power input through the first and second input shafts.