A compact alternating direction implicit(ADI)method has been developed for solving multi-dimensional heat equations by introducing the differential operators and the truncation error is O(τ2 + h4).It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(τ3 + hs)is gained with once Richardson's extrapolation.Some numerical examples are presented to demonstrate the efficiency and accuracy of the new scheme.