Density functional theory calculations were employed to study the mechanism of the Cu-catalyzed alkynylation of the N-sulfonyl α-ketiminoester with phenylacetylene. Based on the characteristics of the terminal alkyne, two possible pathways were proposed and investigated. The favorable reaction pathway includes copper acetylide generation, outer-sphere nucleophilic addition, and protonation. Nucleophilic addition is considered to be the rate-and enantioselectivity-determining step. The oxidative state of Cu(I) remains unchanged in the whole process. The electrophilic attack of the C−C triple bond by the N-sulfonyl ketimine to form the vinyl cation intermediate is shown to be unfavorable. The independent gradient model analysis revealed that the origin of the enantioselectivity comes from the weak hydrogen bond between the ligand and the sulfonamide substrate. Moreover, the side-arm effect controls the enantioselectivity by restricting the distortion of the ligand. This work would be of benefit for the design of new ligands for copper catalysis.