Municipalities output large amounts of solid waste into landfills, but degradation slows during the middle and late stages of treatment. Therefore, accelerating the treatment of degradable substances to achieve rapid stabilization, excavation, screening, and reuse would increase landfill utility and reduce economic costs. This article provides an aerobic degradation model for landfilled municipal solid waste that includes two types of biochemical reactions. Using degradable solid-phase organic matter and ammonia nitrogen as limiting substrates, an equation describing degradation over time was obtained. Both aerobic organic matter hydrolysis and the synchronous nitrification and denitrification reaction followed a kinetic, first-order equation. The influences of temperature, water content, oxygen concentration, and carbon to nitrogen ratio on the kinetic reactions were considered. Similarly, the exothermic reaction characteristics were considered. The model was applied to two previously conducted experiments. The results showed that the model can accurately reflect the degradation laws of various substances under aerobic degradation conditions. SDC and ammonia nitrogen were rapidly degraded and reached very low levels in a short time under aerobic conditions. This indicated that aeration has a significant effect on the degradation of aged waste, which can be used in the accelerated stabilization of aged landfills in the future.