The influence of plastic waste (PW) and fly ash as partial substitutes to coarse aggregate and cement, respectively, and Graphene NanoPlatelets (GNPs) as additive to cement mass on the Cantabro abrasion loss of concrete was investigated in this study. Artificial Neural Network (ANN) and Response Surface Methodology (RSM) techniques were adopted to establish models for estimating the Cantabro loss of the concrete. The variables used were PW, fly ash, GNPs, water-to-cementitious material ratio, and number of revolutions. For the ANN, 60 unique samples of Cantabro loss (%) were used. Fourteen neurons are considered in the hidden layer, and the Levenberg–Marquardt technique is applied to train the network. Both the coefficient of determination (R) and mean square error were taken into consideration for the performance analysis of ANN models to predict the Cantabro loss (%). The present prediction of Cantabro loss (%) by use of the ANN can be a helping source for preceding studies on proposing the solution to utilize PW in concrete. The developed model using RSM also has a very high degree of correlation (R2 = 0.953) and was highly significant. However, in terms of accuracy of prediction, the ANN model was the best, having the highest coefficient of determination with R2 values of 0.995, 0.995, and 0.992 for training, validation, and testing, respectively.