The Sliver elements have serious influences on the quality of mesh generation of centrifugal pump. The position where the Sliver elements may appear in the mesh of centrifugal pump was discussed. The present two main methods to eliminate the Sliver elements were introduced and their advantages and disadvantages were discussed. The algorithm principle of mesh refinement for eliminating the Sliver elements was analyzed in detail. Based on the analysis, it was concluded that the existing refinement algorithms could not completely eliminate the Sliver elements. A relatively good mesh refinement method was improved, and the rule for judging the Sliver elements was modified and optimized. The new method can eliminate the Sliver elements completely and improve the overall mesh quality significantly. The practical applications indicate that the improved algorithm is strict, effective and easy to implement.