Let F be a family of meromorphic functions defined in a domain D,ψ(≠0) be a holomorphic function in D,k is a positive integer.If f∈F,we have f≠0,f(k) +∑（k-1）（i=0）*ai*f(i) does not go to zero,all zeros of ［f(k) +∑（k-1）（i=0）*bi*f(i)］-Ψ(z) have multiplicities at least (k+2)/k,and the differential polynomial ［f(k) +∑（k-1）（i=0）*bif(i)］ and the function ψ(z) have no common zeros,where ai(z) and bi(z) are holomorphic functions in D (i=0,1,…,k-1),then F is normal in D.