We consider solitary-wave solutions of generalized Benjamin-Bona-Mahony- Burgers Equations (shortly BBMB). The decomposition method is proposed for the numerical solution subject to appropriate initial condition. Soliton solutions are constructed to show the nature of the solution. The numerical solutions of our model equation are calculated in the form of convergence power series with easily computable components. The decomposition method performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability. © 2005 Elsevier Inc. All rights reserved.