Understanding the mechanism of the catalytic reaction is an effective way to design new high-performance catalysts. The mechanisms of alkyne/olefin hydrogenations catalyzed by a nonclassical Co-N2 catalyst are explored by ab initio molecular dynamics simulations and density functional theory calculations. From the calculated results, the hydrogenation mechanisms, i.e., molecular or atomic mechanisms, can be effectively controlled via employing the different interaction between the catalyst and substrates. The origination of excellent selectivity toward E-olefins for the Co-N2 catalyst is also taken into account with the help of investigating the olefin hydrogenation process. The mechanism indicates that the negligible energy barrier of rotation is the main reason for highly selective semihydrogenation of a Co-N2 catalyst, which leads to the trans-olefin formation. These investigations may provide some useful information and guidelines on the current understanding of the hydrogenation reaction and designing the high-performance catalysts.