There are about 100 sites of acid mine drainage (AMD) from abandoned/closed mines in Japan. For their sustainable treatment, future prediction of AMD quantity is crucial. In this study, AMD quantity was predicted for two closed mines in Japan based on a series tank model in three stages. The tank model parameters were determined from the relationship between the observed AMD quantity and the inflow of rainfall and snowmelt by using the Kalman filter and particle swarm optimization methods. The Automated Meteorological Data Acquisition System (AMeDAS) data of rainfall were corrected for elevation and by the statistical daily fluctuation model. The snowmelt was estimated from the AMeDAS data of rainfall, temperature, and sunshine duration by using mass and heat balance of snow. Fitting with one year of daily data was sufficient to obtain the AMD quantity model. Future AMD quantity was predicted by the constructed model using the forecast data of rainfall and temperature proposed by the Max Planck Institute–Earth System Model (MPI–ESM), based on the Intergovernmental Panel on Climate Change (IPCC) representative concentration pathway (RCP) 2.6 and RCP8.5 scenarios. The results showed that global warming causes an increase in the quantity and fluctuation of AMD, especially for large reservoirs and residence time of AMD. There is a concern that for mines with large AMD quantities, AMD treatment will be unstable due to future global warming.