We investigated the existence and uniqueness of the cauchy problem of semilinear heat transfer equation. We proved that for α>3，if the initial value φ(x) is sufficiently small in some Sobolev spaces，there exists a unique global classic solution for the Cauchy problem. And the solution decays as t→+∞. The method used in this paper makes the value of α be closely combined with the spaces in which the sloution and initial value function are defined. The larger the value of α is，the better the properties of the solution are.