In this article, we apply the ex−p ( Φ(η))-expansion method for seeking the exact solutions of NLEEs via the (1+1)-Dimensional Compound KdvB equation. Plentiful traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. The obtained results show that e−xp( Φ(η))- expansion method is very powerful and concise mathematical tool for nonlinear evolution equations in science and engineering.