Employing Monte Carlo simulation method, we have studied randomness-induced evolution of the first-order to the second-order phase transition in two-dimensional six-state Potts model system. Biological applications of the Potts model are developed very much recently. We change the transition from first-order to second-order through tuning the bonds strength or the concentration of void bonds. The evolution of phase transition in two-dimensional six-state Potts system is examined with energy histogram and the Binder cumulant analysis.