Adaptive neuro fuzzy inference system (ANFIS) and genetic algorithm–artificial neural network (GA-ANN) models were used to predict the effect of methyl jasmonate (at three levels 0, 0.01, and 0.1 mM) and storage time (0, 14, 28, 42, 56, 70, and 84 days) on quality parameters and physiological changes of pomegranate fruits during storage. Methyl jasmonate reduced chilling injury and improved quality characteristics of pomegranates during postharvest storage. The GA-ANN and ANFIS were fed with two inputs of methyl jasmonate and storage time. The results showed that GA-ANN predictions agreed with experimental data and the GA-ANN with 14 neurons in one hidden layer can predict physiological changes and quality parameters of pomegranate (weight loss, pH, chilling injury index, ion leakage, ethylene, respiration, polyphenols, anthocyanins, and total antioxidant activity) with correlation coefficients equal to 0.87. The ANFIS model was trained by a hybrid method and agreement between experimental data and ANFIS predictions was significant (r = 0.90).