Performance of neural networks depends upon several input parameters. Several attempts have been made for optimization of neural network parameters using Taguchi methodology for achieving single objective such as computation effort, computation time, etc. Determination of optimum setting to these parameters still remains a difficult task. Trial-and-error method is one of the frequently used approaches to determine the optimal choice of these parameters. Keeping in view the problems with trial-and-error method, a systematic approach is required to find the optimum value of different parameters of neural network. In the present work, three most important distinct performance measures such as mean square error between actual and prediction, number of iteration, and total training time consumption have been probably considered first time concurrently. The multiobjective problem has been solved using Grey–Taguchi methodology. In this study, optimal combinations of different neural network parameters have been identified by using the Taguchi-based Grey relational analysis. The data set includes 81 sets of milling data corresponding to three-level full factorial experimental design for four cutting parameters, i.e. cutting speed, feed, axial depth of cut, and radial depth of cut, respectively. The output is average surface roughness for the experiment. The performance of different neural network models has been tabulated in L36 orthogonal array. Confidence interval has also been estimated for 95% consistency level to validate the optimum level of different parameters. It was found that the Taguchi-based Grey relational analysis approach can effectively be used as a structured method to optimize the neural network parameters settings, which can be easily implemented to enhance the performance of the neural network model with a relatively small size and time saving experiment. The result clearly indicates that the optimal combination of neural network parameters obtained by using the proposed approach performs better in terms of low mean square error, small number of iterations, and lesser training time required to perform the analysis which further results in lesser computation effort and processing time. Methodology proposed in this work can be utilized for any type of neural network application to find the optimum levels of different parameters.