In this paper, we employ the extended tanh function method to find the exact traveling wave solutions and solitary wave solutions involving parameters of the Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. These studies reveal that the Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-law nonlinearity has a rich variety of solutions.