The esterification of acidified oil with ethanol under microwave radiation was modeled and optimized using response surface methodology (RSM) and artificial neural network (ANN). The impacts of mass ratio of ethanol to acidified oil, catalyst loading, microwave power and reaction time are evaluated by Box-Behnken design (BBD) of RSM and multi-layer perceptron (MLP) of ANN. RSM combined with BBD shows the optimal conditions as catalyst loading of 5.85 g, mass ratio of ethanol to acidified oil of 0.35 (20.0 g acidified oil), microwave power of 328 W and reaction time of 98.0 min with the free fatty acids (FFAs) conversion of 78.57%. Both of the models are fitted well with the experimental data, however, ANN exhibits better prediction accuracy than RSM based on the statistical analyses. Furthermore, membrane vapor permeation and in-situ molecular sieve dehydration were investigated to enhance the esterification under the optimized conditions. (C) 2016 Elsevier Ltd. All rights reserved.