This paper is concerned with the problem of quantized H-infinity control for networked control systems (NCSs) with time-varying delay and multiple packet dropouts. The packet dropouts in both the measurement channel and the control channel are considered simultaneously, and are modeled as stochastic variables with Bernoulli random binary distribution. Both the control input and measurement output are quantized before transmission and the quantization errors are described as sector-bound uncertainties. Sufficient conditions for the existence of an observer-based, delay-dependent controller are developed to ensure the exponentially mean-square stability of the closed-loop system and to achieve the optimal H-infinity disturbance attenuation. A numerical example is given to illustrate the effectiveness of the proposed method.