  A smooth scheme X over a field k of positive characteristic is said to be
strongly liftable, if X and all prime divisors on X can be lifted
simultaneously over W_2(k). In this paper, we give some concrete examples and
properties of strongly liftable schemes. As an application, we prove that the
Kawamata-Viehweg vanishing theorem in positive characteristic holds on any
normal projective surface which is birational to a strongly liftable surface.
