Flows in a spouted bed in a cylinder with a tapered bottom were simulated numerically. To reduce the computational load, a quasi-three-dimensional numerical simulation method for axisymmetric gas-solid flows was proposed. Fluid motion was calculated two-dimensionally by solving the locally averaged equations written in cylindrical coordinates, in which the circumferential components were neglected assuming the axisymmetry. Particle motion was calculated three-dimensionally and was traced discretely by solving Newton's equation of motion for each particle. The discrete element method (DEM) was employed to model the interaction between particles. The typical flow pattern of the spouted bed was obtained in the present calculation, i.e., a stable spout, fountain and annulus were obtained. The calculation was made for the same geometry as the experiment by Roy et al. [D. Roy, F. Larachi, R. Legros, J. Chaouki, Can. J. Chem. Eng. 72 (1994) 945-952]. The calculated spout diameter agreed quantitatively well with their experimental result. The calculated distributions of the vertical component of the particle velocity in the spout, the fountain and the annulus were compared with the experiments by He et al. [Y.-L. He, S.-Z. Qin, C.J. Lim, J.R. Grace, Can. J. Chem. Eng. 72 (1994) 561-568], in which smaller particles were used. The calculated velocity profiles agreed qualitatively well with the experimental results in spite of the difference in the particle diameter.