The effective study of hybrid machining processes (HMPs), in terms of modeling and optimization has always been a challenge to the researchers. The combined approach of Artificial Neural Network (ANN) and Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) has attracted attention of researchers for modeling and optimization of the complex machining processes. In this paper, a hybrid machining process of Electrical Discharge Face Grinding (EDFG) and Diamond Face Grinding (DFG) named as Electrical Discharge Diamond face Grinding (EDDFG) have been studied using a hybrid methodology of ANN-NSGA-II. In this study, ANN has been used for modeling while NSGA-II is used to optimize the control parameters of the EDDFG process. For observations of input-output relations, the experiments were conducted on a self developed face grinding setup, which is attached with the ram of EDM machine. During experimentation, the wheel speed, pulse current, pulse on-time and duty factor are taken as input parameters while output parameters are material removal rate (MRR) and average surface roughness (R_a). The results have shown that the developed ANN model is capable to predict the output responses within the acceptable limit for a given set of input parameters. It has also been found that hybrid approach of ANN-NSGA-II gives a set of optimal solutions for getting appropriate value of outputs with multiple objectives.