  In this paper, we consider the stability of quermassintegral inequalities
along a inverse curvature flow. We choose a special rescaling of the flow such
that the $k$-th quermassintegral is decreasing and the $k-1$-th
quermassintegral is preserved. Along this rescaled flow, we prove that the
decreasing rate of the $k$-th quermassintegral is faster than the Fraenkel
asymmetry of the domain when approaching to the sphere. This leads to the
stability inequality of quermassintegral inequalities for nearly spherical sets
using the flow method.
