Networked control system (NCS) is a multidisciplinary area that attracts increasing attention today. In this paper, we deal with remote supervision of a nonlinear networked control systems class subject to network imperfections. Different from many existing researches that consider only the problem of small and/or constant communication delays, we focus on large and time-varying network delays problem in both measurement and control channels. The proposed method is a set-membership estimation-based predictor approach computing a guaranteed set of admissible state values when the uncertainties (i.e. measurement noises and system disturbances) are considered unknown but bounded with a priori known bounds. The state prediction strategy is used to compensate the effect of transmission delays. Finally, the theoretical results are validated through a numerical example.