The dynamics of quantum discord for a class of qutrit-qutrit states under depolarizing and dephasing noise are investigated using the geometric measure of quantum discord.We find that in the quantum discord for these states,a sudden change near the transition point exists from a bound-entangled to a free-entangled state,and that the sudden change point remains unchanged in later evolution under depolarizing noise.Moreover,the behavior of quantum discord is independent of the parameter of the given initial states in many regions.