An Eulerian-Lagrangian computational model for simulations of gas-liquid-solid flows in three-phase slurry reactors is developed. In this approach, the liquid flow is modeled using a volume-averaged system of governing equations, whereas motions of bubbles and particles are evaluated by Lagrangian trajectory analysis procedure. It is assumed that the bubbles remain spherical and their shape variations are neglected. The two-way interactions between bubble-liquid and particle-liquid are included in the analysis. The discrete phase equations include drag, lift, buoyancy, and virtual mass forces. Particle-particle interactions are accounted for by the hard sphere model approach. The bubble collisions and coalescence are also included in the computational model. The simulation results show that the transient characteristics of the three-phase flow in a column are dominated by time-dependent staggered vortices. The bubble plume moves along a S-shape path and exhibit an oscillatory behavior. While most particles are located outside the vortices, some bubbles and particles are retained in the vortices. Bubble upward velocities are much larger than both liquid and particle velocities. Particle upward velocities are slightly smaller than the liquid velocities.