Pork supply prediction is a challenging task of significant importance for pig producers and administrators, as it aids decision-making and maintains the pork supply–demand balance. Previous studies failed to consider impact factors like the month-age transfer principle of pigs, epidemic factors, and the simultaneous import and export volumes of pork, leading to the absence of a quantitative prediction model for pork supply. In this background, we proposed a novel quantitative prediction model of pork supply that incorporates pork production and pork import/export volumes. First, a prediction model for pork production that takes into account the month-age transfer principle of pigs and epidemic factors was presented, along with a recursive model of the pig-herd system. A novel method based on a modified self-organizing migrating algorithm (MSOMA) was proposed for calculating the quantity of monthly newly retained sows (NRS). Furthermore, the pork-production prediction model considered the epidemic factor as a random disturbance term (RDT), and a prediction method based on MSOMA and a back-propagation neural network (MSOMA-BPNN) was introduced to predict such disturbance terms. Second, the proposed MSOMA-BPNN was employed to predict pork import and export volumes. The pork supply was subsequently determined based on the predicted pork production, as well as the pork import and export volumes. The proposed pork supply prediction model was applied to forecast China’s pork supply from 2010 to 2023. The results validate the high effectiveness and reliability of the proposed model, providing valuable insights for decision makers. The empirical results demonstrate that the proposed model is a promising and effective tool for predicting the pork supply. To our knowledge, this is a novel tool for pork supply prediction, considering the pig-herd system and pork import and export volumes from a systemic perspective. These features allow for consideration of the scientific formulation of a pig production plan, the establishment of early warning mechanisms to deal with epidemic situations and emergencies, and the regulation of pork supply and demand balance.