In this study, we dealt with conservation laws and exact travelling wave solutions of viscous Burgers equation. We used conservation theorem for finding conservation laws for this equation. All founded conservation laws are trivial conservation laws. Then, we found the exact solutions of viscous Burgers equation using the exponential rational function method. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear partial differential equations. Also the obtained results are shown graphically.