With the aid of density functional theory(DFT)calculations,we have investigated the mechanisms and stereoselectivities of the DMAP-catalyzed [2+4] cycloaddition reaction of γ-methyl allenoate R1 with phenyl(phenyldiazenyl)methanone R2.Various possible reaction pathways are analyzed and discussed.The results of the DFT calculations show that the preferred mechanism(mechanism A)includes four steps: the first step is the nucleophilic addition of DMAP to R1 to form the zwitterionic intermediate 1,the second step is the γ-addition of 1 to R2 to generate intermediates γ-2(R&S),the third step is the intramolecular Michael addition to give the six-membered ring intermediates γ-3(RR&SS),and the last step is the catalyst DMAP liberation from γ-3(RR&SS)to generate the final product γ-P(R&S).The addition of DMAP to R1 is calculated to be the rate-determining step.The reaction of 1 with R2 is the stereoselectivity-determining step.The calculated results are in good agreement with experimental findings.The present study may provide a useful guide not only for understanding other analogous reactions but also for designing new reactions in the future.