  A maximum jet efficiency line $R\sim 25$ ($R=L_{\rm jet}/L_{\rm bol}$), found
in FRII radio galaxies by Fernandes et al., was extended to cover the full
range of jet power by Punsly. Recent general relativistic magnetohydrodynamic
(GRMHD) simulations on jet formation mainly focused on the enhancement of jet
power. In this work, we suggest that the jet efficiency could be very high even
for conventional jet power if the radiative efficiency of disk were much
smaller. We adopt the model of a thin disk with magnetically driven winds to
investigate the observational high efficiency jets in FRII radio galaxies. It
is found that the structure of a thin disk can be significantly altered by the
feedback of winds. The temperature of disk gradually decreases with increasing
magnetic field; the disk density, surface density and pressure also change
enormously. The lower temperature and higher surface density in inner disk
result in the rapid decrease of radiative efficiency. Thus, the jet efficiency
is greatly improved even the jet power is conventional. Our results can explain
the observations quite well. A theoretical maximum jet efficiency $R \sim 1000$
suggested by our calculations is large enough to explain all the high jet
efficiency in observations even considering the episodic activity of jets.
