Let ψ(z) be a holomorphic function in a domain D,which is not identical to zero,and all of whose zeros are simple,k be a positive integer, and F be a family of meromorphic functions in a domain D. If for each f of F,f≠0 and all poles of f are multiple; for each pair of functions f and g in F,their differential polynomials share ψzin D,then F is normal in D.