A power transmission apparatus for a vehicle is disclosed. The power transmission apparatus includes three concentric input shafts, input shaft fixedly connected to an engine output shaft, a transmitting shaft disposed on the outer circumference of the first input shaft without rotation interference, a central shaft parallel to a first one of the input shafts and spaced apart from the first input shaft by a predetermined interval, a fixed transmission selectively shifting an input torque depending on the respective gear ratios of four change gear trains disposed between first and second input shafts, the transmitting shaft, and the central shaft and each having drive gears and driven gears externally connected to each other and outputting the shifted torque through the central shaft and the transmitting shaft, and composite transmission including a planetary gear set having a sun gear fixedly connected to one side of the transmitting shaft.