Many nonlinear partial differential equations admit traveling wave solutions that move at a constant speed without changing their shapes. It is very important and difficult to search the exact travelling wave solutions.In this work, the auxiliary Riccati equation method and the computer symbolic system Maple are used to study exact solutions for the nonlinear Kuramoto-Sivashinsky equation. Maple can help us solve tedious algebraic calculation. Therefore many exact traveling wave solutions are successfully obtained which include some new kink (or anti-kink) wave solutions and periodic wave solutions.