Honeybee population dynamics and prediction is the core content of honeybee population ecology research, which is closely related to the development of agriculture, economy and other industries. This paper aims to study honeybee population dynamics and pollination prediction. Firstly, a differential equation model is proposed to analyze the number of bees in a single beehive in detail, and the Elman model is used to further validate it. Then, through a sensitivity analysis of bee colony size, the main factors affecting hive colony size were identified: the egg-laying rate and the number of varroa mites. Furthermore, combined with the differential equation model, a beehive prediction model for crop pollination was constructed, which can predict the number of beehives required for crop pollination on a 20-acre (81,000) land. At the same time, the effect of initial beehive colony size on the number of beehives required for pollination of different plants in a given area was studied in depth. The usefulness and applicability of our model is well demonstrated by the reasonable trend and prediction results of colony size obtained by applying the model to real data. Finally, the paper provides an outlook on future research and improvement directions in this field.