A power transmission apparatus for a hybrid electric vehicle includes: a planetary gear set including first, second and third rotary elements; a first shaft fixedly connected to an output shaft of an engine; a second shaft fixedly connected to the first rotary element and a first motor/generator; a third shaft receiving rotational power from the first shaft; a fourth shaft selectively connected with the first shaft, and the fourth shaft selectively receiving rotational power from the first shaft or from the third rotary element; a fifth shaft fixedly connected to a second motor/generator; and a sixth shaft transmitting rotational power transmitted from the fifth shaft to a final reduction gear of the differential gear. In particular, the six shafts are connected to external gears mutually by four gear sets so that rotational power is transmitted.