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In this paper, a novel predictive control-based approach is proposed for a networked control system with random delays containing an input nonlinear process based on a Hammerstein model. The method uses a time-delay two-step generalized predictive control scheme, which consists of two parts: one is to deal with the input nonlinearity of the Hammerstein model and the other is to compensate for the network-induced delay in the networked control system. A theoretical result using the Popov criterion is presented for the closed-loop stability of the system in the case of a constant delay. Simulation examples illustrating the validity of the approach are also presented.