We made linearization stability analysis on traveling wave solutions of KdV-Burgers equation. Numerical results indicate that traveling waves are dynamically stable for positive-dissipation case, while they are dynamically unstable for negative-dissipation case. Then we presented a finite difference scheme, which is conditionally stable, for long-time evolution of perturbed traveling waves. Numerical results also show that traveling waves are dynamically stable as positive-dissipation is held. Our results modify and improve conclusions given in relative literatures.