A numerical prediction for the axial and swirling pneumatic conveying in a vertical pipe was performed based on an Eulerian approach for the gas and a stochastic Lagrangian approach for the particles, where k - epsilon turbulence model, the model of particle-particle and particle-wall collisions, was adopted. The numerical results are presented for polyethylene pellets of 3.2mm diameter conveyed through a pipeline of 12 m in height with an inner diameter of 80 mm. The initial swirl number was 0.0 and 0.68, the mean gas velocity varied from 11 to 17m/s, and the solid mass flow rate was 0.03 and 0.084 kg/s. From the numerical analysis, the swirl decay of the swirling gas-solid flow was found to be rapid in the acceleration region and approached the clean swirling flow in a fully developed region. The turbulent kinetic energy and energy dissipation rates of the swirling gas-solid flow increased near the wall and reduced in other regions. The comparison of predicted values with measured data showed a good agreement.