A transient mathematical model based on continuity equations for liquid and gas phases, with a momentum equation for the mixture, was developed, and numerical solutions and simulations corresponding to severe slugging in pipeline-riser system were presented, and the results were compared with the experimental data to verify the mathematical model. In numerical solutions, backward Euler schemes were adopted as predictors and trapezoidal methods were used as correctors. Variable time steps were employed for higher computational efficiency and accuracy in the integration. Experiments of severe slugging characteristics were performed, and the simulation results of the cycle periods and bottom pressure were compared with experimental values. Finally, the calculation results of detailed characteristics were analyzed thoroughly. The results show that the developed mathematical model can accurately predict the cycle time and the detailed characteristics of severe slugging. Under the experimental conditions, the liquid slug length can reach 1.6 times the height of the riser, and the maximum instantaneous gas velocity of outlet is 50 times the inlet gas velocity, and the maximum instantaneous liquid velocity of outlet is 28 times the inlet liquid velocity, having important implications for the hazard assessment of severe slugging.