Due to the finite source of fossil fuels and their high emissions, it is remarkable to recognize appropriate ways to produce alternative fuels with less pollution. In this paper, the production of biodiesel (fatty acid methyl ester) from transesterification of methanol with sesame oil under ultrasound-assisted waves (using a homogeneous sodium hydroxide catalyst) was investigated. In addition, the optimization and prediction of biodiesel production was studied and compared with the two methods of response surface methodology (RSM) and the combined model of artificial neural network (ANN) – particle swarm algorithm (PSO). The central composite design (CCD) was used to investigate the effect of independent variables (methanol/oil molar ratio, catalyst percentage, reaction time and temperature) on the yield of biodiesel in Expert Design software. Analysis of experimental results was performed using RSM and ANN–PSO hybrid methods and also the optimal conditions for maximizing the yield were calculated. The highest yield of biodiesel predicted by RSM and ANN–PSO were 87.4 and 90.58%, respectively. RSM and ANN–PSO hybrid models were compared based on least squared errors statistically. The correlation coefficients in the RSM and ANN–PSO hybrid models were 0.959 and 0.999 respectively. While both models demonstrated a good agreement with actual results, but the ANN–PSO hybrid model had a powerful prediction for the optimal points over the RSM.