In this paper, we are concerned with the quantized H∞ control problem for a class of stochastic systems with random communication delays. The system under consideration involves signals quantization, Itô stochastic disturbance as well as random communication delays. The measured output and the control input quantization are considered simultaneously. We aim at designing an observer-based controller such that the dynamics of the filtering error is guaranteed to be exponentially stable in the mean square, and a prescribed H∞ disturbance attenuation level is also achieved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.