In this paper ，a new property of transcendental integral functions has been proved by making use of Hadamard，s three-circle theorem and a character of maximum principle of integral function f(z) which is defined in circumference |z|=r,i．e．lim[DD(][]n∞[DD)][SX(]M(r)[]M(kr)[SX)]=0,wherek＞1 ．