A power transmitting apparatus may include: an input device including a motor shaft selectively connected to an engine, a first input shaft selectively connected to the motor shaft and provided with at least one input gear fixedly disposed thereon, and a second input shaft disposed without rotational interference with the first input shaft and provided with at least one input gear fixedly disposed thereon; a motor/generator disposed on the motor shaft of the input device and operated as a motor or a generator; a selectively connecting device adapted to selectively connect the motor shaft of the input device to the engine, the first input shaft, or the second input shaft; and a speed output device changing torque input from the first and second input shafts of the input device and outputting the changed torque.