The influence of Group 15 elements (G15s) on the reactivity of the cycloaddition reactions of inorganic 1,3-dipolar analogs with cyclooctyne was computationally explored with density functional theory. To this end, the G15G15G15'-based 1,3-dipole, an interestingly representative model molecule of 1,3-dipole chemistry, was selected. The present computational investigations suggest that all NNG15-Rea and G15G15P-Rea molecules can be energetically feasible to undergo 1,3-dipolar cycloaddition reactions with cyclic alkynes, except for only the NNN-Rea 1,3-dipole molecule. The key factor, which can greatly affect the activation barriers, is quantitatively analyzed in detail through the frontier molecular orbital (FMO) theory, the activation strain model (ASM), and the energy decomposition analysis (EDA) approach. Our theoretical findings based on the FMO theory and the EDA suggest that two types of bonding interactions occur in such 1,3-dipolar cycloaddition reactions: forward bonding (filled p-π orbital (cyclooctyne) → the empty p-π* orbital (G15 = G15)) and back bonding (empty p-π* orbital (cyclooctyne) ← the lone pair (G15')). Notably, the bonding interactions of the former mechanism are much stronger than those of the latter mechanism. Evidence from the ASM reveals that the activation barriers of G15G15G15'-based 1,3-dipolar cycloaddition reactions strongly depend on the atomic radius of the G15 element. These theoretical conclusions allow a number of predictions to be made.