With the theory of Pang-Zalcman,The author studies the normal family of meromorphic functions and a normal theorem is proved,which generalizes and improves the results of Fang Ming-Liang:let F be a family of holomorphic functions on plane domain D,α≠0,b∈C,if f∈F,(f(k)(z))′-α(f(z))m≠b,and the zeros of 〗fare of multiplicity at least k+2,and then F is normal on D.