Efficient power optimization of Brayton heat engine with variable specific heat of the working fluid is analyzed from the view of finite time thermodynamics. The efficient power is defined as the multiplication of engine power and engine efficiency. Hence, the proposed method considers not only the power output but also the engine efficiency. Optimizing the efficient power gives a compromise between power and engine efficiency. Results obtained are compared with those obtained by using the maximum power (MP) and maximum power density (MPD) conditions. The results show that the engine designed at maximum efficient power (MEP) criterion is more efficient as compared with those designed at maximum power and maximum power density conditions. The system analysis is done with variable specific heat parameter due to which its performance is comparable to the real systems. Moreover, engine designed at maximum efficient power criterion requires lesser pressure ratio over those designed at maximum power density conditions. Brayton heat engine with variable specific heat of the working fluid gives realistic prediction of engine efficiency and engine power than does the isentropic Brayton heat engine with constant specific heat.