A high-order alternating direction implicit(ADI) method for solving two or three dimensional heat equations is proposed.The method is fourth order in space and second order in time.A von Neumann analysis shows that the method is unconditionally stable.It permits to use TDMA algorithm with a considerable save of computing time.Numerical experiments are conducted to test its high accuracy and to compare it with the second order Peaceman-Rachford scheme,Doulgas scheme and Crank-Nicolson scheme.