With Computational Fluid Dynamics (CFD) software FLUENT, the flow characteristics of an elbow of the West-east oil pipelines was analyzed. The results of the velocity vector-graph and fluid pressure distribution of the elbow were also obtained. The distribution of fluid pressure on elbow wall was found. Furthermore, the secondary flow can be precisely predicted with the proposed procedures. The analysis results provide mechanics analysis foundation for improvement of strength design and processing technic of elbow.