With the aid of the Lax Niouver transformation,the exact travelling wave solutions and the asymptotic travelling wave solutions of the KdV Burgers Equation are obtained.Furthermore,the series solutions are constructed with the Adomian integration.The relations of the travelling wave solutions between the KdV Burgers equation and the RLW Burgers equation are found.Moreover,a class of known exact solutions of the KdV Burgers equation are analysed.