In this paper we address the stabilization problem of the nonlinear feedback systems with quantized measurements in the presence of bounded disturbances. Building on an approach applied in [Liberzon, Nesic, 2004] to the linear time-invariant systems with quantized feedback, we extend the results of [Kameneva, Nesic, 2008] to the quantized control systems with nonlinear dynamics. Using the time-sampled scheme proposed in [Liberzon, Nesic, 2004] and later used in [Kameneva, Nesic, 2008], we show that the nonlinear gain h stability is achievable for the nonlinear systems with quantized feedback.