A power transmission apparatus for a vehicle may include a first shift module configured to change torque input from an engine into four speed stages and to output the four speed stages, a motor/generator directly connected an output side of the first shift module, a second shift module configured to change the four speed stages input from the first shift module into eight speed stages by using a planetary gear set and to output the eight speed stages, and an output device connected to an output side of the second shift module through an output shaft.