This invention relates to a heterogeneous copper nanocatalyst composed of copper nanoparticles immobilized on a boehmite support, a method of preparing the same, and the use thereof. The copper nanocatalyst composed of the copper nanoparticles supported on boehmite exhibits excellent performance in a Huisgen cycloaddition reaction and an A3 coupling reaction of aldehyde, amine and alkyne. The copper nanocatalyst is able to be prepared in a large scale and shows superior reactivity even when used in a small amount under mild conditions without an additive in an organic reaction. This heterogeneous catalyst is easy to separate and reuse after the reaction.