In this paper, the quadratic B-spline collocation method is implemented to find numerical solution of the Benjamin-Bona-Mahony-Burgers (BBMB) equation. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. Also the convergence of the method is proved. The method is applied on some test examples, and numerical results have been compared with the exact solution. The numerical solutions show the efficiency of the method computationally.