  Recently, biased weak measurement(BWM) has shown higher precision than both
conventional measurement and standard weak measurement(SWM) in optical
metrology. In this paper, we propose a scheme of detecting rotation velocity in
Sagnac's interferometer with BWM. In particular, BWM employs an additional
reduction of photons in the post-selection by introducing a pre-coupling, and
the remaining photons have been shown to be extremely sensitive to the
estimated parameter. In addition, our numerical results show that the scheme
with BWM can obtain a higher sensitivity than the scheme with SWM.
