Continuous dissolution of spent fuel is indeed one of the key technologies that can significantly improve the efficiency and stability of spent fuel reprocessing. The China Institute of Atomic Energy designed a prototype rotary drum dissolver, and the dissolution behavior of UO2 pellets in the dissolver was calculated using the Discrete Element Method. A kinetic equation was established to model the dissolution behavior, considering variables such as temperature, nitric acid concentration, and stirring intensity. The calculations showed that complete pellet dissolution took about 10 h in the continuous reaction, compared to 6 h in the batch dissolution experiment due to the gradual decrease in nitric acid concentration. A 16 h continuous dissolution experiment confirmed the calculated results, with a deviation of 10.8% between the simulation and experiment in terms of the mass of dissolved pellets. It was also found that it takes approximately 30 h to reach equilibrium in the continuous rotary dissolver, with a nitric acid concentration of 2.8 mol/L and a uranium concentration of 243 g/L at equilibrium.