A power transmitting apparatus may include a first input shaft to selectively receive torque of an engine, a second input shaft having at least one input gear fixedly disposed thereon, a third input shaft having at least one input gear fixedly disposed thereon, a motor/generator operated as a motor or a generator, a planetary gear set including a first rotation element directly connected to the motor/generator, a second rotation element directly connected to the third input shaft, and a third rotation element directly connected to the first input shaft, a first speed output unit to convert torque input from the second input shaft or the third input shaft and output the converted torque, and a second speed output unit to convert torque input from the second input shaft or the third input shaft and output the converted torque.