A new method is presented for the numerical solution of Burgers' equation. In this method, the Green's function of the linear heat conduction equation is employed to convert Burgers' equation to the corresponding integration equation system with respect to the time variable. Then the solution of this integration system is obtained by a numerical method. The computed results show that this method can deal with a wide range of Reynolds number and in the moderate Reynolds number case, even with the comparatively larger time step, good accuracy can be achieved. Furthermore, this method does not require spatial discretization. Copyright © 2001 John Wiley & Sons, Ltd.