The reaction mechanism between azacyclopropenylidene and epoxypropane has been systematically investigated employing the second-order M${o}$ller-Plesset perturbation theory (MP2) method to better understand the reactivity of azacyclopropenylidene with four-membered ring compound epoxypropane. Geometry optimization, vibrational analysis, and energy property for the involved stationary points on the potential energy surface have been calculated. It was found that for the first step of this reaction, azacyclopropenylidene can insert into epoxypropane at its C-O or C-C bond to form spiro intermediate IM. It is easier for the azacyclopropenylidene to insert into the C-O bond than the C-C bond. Through the ring-opened step at the C-C bond of azacyclopropenylidene fragment, IM can transfer to product P1, which is named as pathway (1). On the other hand, through the H-transferred step and subsequent ring-opened step at the C-N bond of azacyclopropenylidene fragment, IM can convert to product P2, which is named as pathway (2). From the thermodynamics viewpoint, the P2 characterized by an allene is the dominating product. From the kinetic viewpoint, the pathway (1) of formation to P1 is primary.