  A smooth scheme $X$ over a field $k$ of positive characteristic is said to be
strongly liftable over $W_2(k)$, if $X$ and all prime divisors on $X$ can be
lifted simultaneously over $W_2(k)$. In this paper, we give a criterion for
that cyclic covers over strongly liftable schemes are still strongly liftable.
As a corollary, cyclic covers over projective spaces of dimension at least
three are strongly liftable over $W_2(k)$.
