Abstract: A normality criterion for a family of holomorphic functions was got. Let F be a family of holomorphic functions on the unit disk ⊿, all of whose zeros are of multiplicity at least m; let M,N be two positive numbers; if for any f∈F, f(z)=0
=> |f^(m)(z)| _^≦M ,f^(m)(z)=1 => |f(z)| ≧N , then F is normal on ⊿.

Key words: entire function, holomorphic function, normal family, entire function, holomorphic function