In this paper, we obtain the following normal criterion: Let F be a family of meromorphic functions in domain D C, all of whose zeros have multiplicity k + 1 at least. If there exist holomorphic functions a(z) not vanishing on D, such that for every function f(z) ∈ F,f(z) shares a(z) IM with L(f) on D, then F is normal on D, where L(f) is linear differential polynomials of f(z) with holomorphic coefficients, and k is some positive numbers. We also proved coressponding results on normal functions.