In this paper, the H∞ synchronization of general chaotic systems with random perturbations is investigated, in which perturbation is a random process of Brownian motion. Based on stochastic Lyapunov stability theory, linear matrix inequalities, and It formula and H∞ control method combined with feedback control laws, some new asymptotic synchronization schemes are established which guarantee robust stochastical mean square asymptotical synchronization for drive system and noise-perturbed response system, as well as achieving a prescribed stochastic robust H∞ performance level. These schemes are in a simple form and easy to work with Matlab. Finally, simulations show that the proposed results are correct and effective.