In this study, we explore an a new crosslinker (bis-butyl succinate, BBS) with terminal alkyne group to react with glycidyl azide polymer-based polyurethane (original PU) via “azide-alkyne” click reaction, which has supported enhancing mechanical properties and cross-link densities of modified PUs with BBS. Besides, this crosslinker has been designed and synthesized successfully via an esterification reaction to can incorporate with the original PU through the formation of 1,2,3-triazole groups. Moreover, the mechanical properties of resultant modified PUs are investigated to indicate a relationship of mole ratio of [C≡C]/[N3] and cross-link density. Specifically, the stress and Young’s modulus of the modified PUs increase, whereas their strain decrease on increasing the synthesized BBS content regarding to the increased rigid 1,2,3-triazole networks, as well as the cross-link densities of the modified PUs increase with the BBS content through the Mooney-Rivlin equation. As such, there is an enhancement in the mechanical behaviors of the original PU cross-linked with BBS.