The discharge of untreated wastewater containing dyes causes water pollution. The present study evaluated the simultaneous removal efficiency of Reactive Violet 5 (RV5) and Acid Red 98 (AR98) utilizing nanosized zero-valent iron (nZVI) incorporated with chitosan (CS) and copper (Cu) (nZVI-CS-Cu) as a novel adsorbent for the concurrent elimination of mentioned dyes. Identification of the synthesized adsorbent was studied by SEM, EDX, FTIR, XRD, and BET. The amorphous structure of nZVI-CS-Cu was proven by XRD (2θ = 44˚). The BET surface area was 110.53 m2g−1. Solution pH, adsorbent dosage, contact time, initial concentration of dye, and temperature were various factors for investigating their effects on the adsorption process using central composite design (CCD). To obtain this, a linear model was selected as the best model. According to the findings, at the optimum conditions, including pH of 3.0, sorbent dosage of 0.3 g, contact time of 15 min, dye concentration of 20 mg/L, and temperature of 40 ˚C, the maximum removal efficiency was 87.80% (actual) and 87.97% (predicted). In the CCD model, adjusted R2 and R2 predicted were 0.9670 and 0.9634, respectively. The significance of the model was confirmed by the F-value of 288.56 and a p-value < 0.0001. Feed-forward back propagation neural network (FFBP-NN) with Levenberg–Marquardt (LM) and scaled conjugate gradient (SCG) as training algorithms were applied for predicting the percentage of dye removal. After testing different layers (2 and 3) and neurons (2, 3, 4, 5, 6, 7, 8, 9), the neurons of 8 in hidden layer 3 with mean square error (MSE) of 4.01 × 10–20 for the LM algorithm, and neurons of 7 in the layer of 3 with MSE of 1.18 for the SCG algorithm were selected as the best layers and neurons. Excellent modeling with percent recovery close to 100 for LM (training: 100.68%, validation: 100.89%, and testing: 100.85%) and SCG (training: 100.20%, validation: 99.84%, and testing: 100.13%) was obtained. The Langmuir model with R2 of 0.9993 and qmax of 52.91 mg/g and pseudo-second-order kinetics with R2 of 0.9996 followed the adsorption isotherm and kinetic, respectively. It can be said that the proposed adsorbent is simple and economical with good performance, which can be used to remove different dyes from wastewater.