In this paper, we propose a new intelligent sensor based on Electrolyte-Gated Graphene Field-Effect Transistor (EGG-FET) and Artificial Neural Network (ANN)-based Corrector, for high performance and low cost pH monitoring applications. The EGG-FET behavior is investigated analytically using an analytical drain current model based on drift-diffusion carrier transport which is given as function of chemical, electrical, and dimensional sensor parameters. The sensitivity of the EGG-FET is studied under different electrolyte compositions which comprise essentially the ionic strength, pH, and type of ions. The obtained results are verified with experimental data, and a good agreement is achieved. Furthermore, a correction component (Corrector) based on ANN technique is developed using the Levenberg-Marquardt (LM) training algorithm in order to compensate the effect of salt concentration fluctuations on pH sensor response, improve the sensitivity, and correct the sensor nonlinearity. The smart sensor is simulated in dynamic electrolytic environment, and its response is found linear and independent of changes in the electrolyte composition. A similar approach can be followed for the study and development of various EGG-FET-based intelligent biosensors.