This paper aims to study on feedback control for a networked system with both uncertain delays and, packet dropouts and disturbances. Here, a so-called robust predictive control (RPC) approach is designed as follows: 1) delays and packet dropouts are accurately detected online by a network problem detector; 2) a so-called proportional-integral-based neural network grey model (PINNGM) is developed in a general form to be capable of forecasting accurately in advance the network problems and the effects of disturbances on the system performance; 3) using the PINNGM outputs, a small adaptive buffer (SAB) is optimally generated on the remote side to deal with the large delays and/or packet dropouts and, therefore, simplify the control design; 4) based on the PINNGM and SAB, an adaptive sampling-based integral state feedback controller is simply constructed to compensate the small delays and disturbances. Thus, the steady-state control performance is achieved with fast response, high adaptability, and robustness. Case studies are finally provided to evaluate the effectiveness of the proposed approach.