Anaerobic batch co-digestion of mango leaves (ML) and pig manure (PM) at 37 °C with five different ML:PM ratios (1:0, 3:1, 1:1, 1:3, and 0:1) was evaluated for the first time. Five different kinetic models were used (first-order kinetic, cone, modified Gompertz, logistic, and transference models) to find the kinetic parameters for the co-digestion of ML and PM. The methane production results proved that the addition of PM highly improved the ML methane production; the highest biodegradability and methane yield of 86% and 465 mL CH4 g−1 VS, respectively, were obtained at ML:PM ratio of 1:3, which were 160%, 26.5%, 19%, and 72% and 196%, 37%, 24%, and 66% higher than those of 1:0, 3:1, 1:1, and 0:1 mixing ratios, respectively. The cone model (as proved by low root mean square error (RMSE) and Akaike’s Information Criterion (AIC)) showed a better fit to the experimental data. The results of the present work showed the synergistic effect of co-digestion to enhance anaerobic degradation of mango leaves and pig manure for biogas production, providing a practical basis for an energy-efficient strategy for bio-waste management.