An air-stable N-heterocyclic carbene–copper thiophene-2-carboxylate (CuTC) complex has been prepared for the stereoselective hydroboration of terminal alkynes using pinacolborane (HBpin) or 1,8-naphthalenediaminatoborane (HBdan). The newly synthesized complex can be directly activated by hydroboranes without a cocatalyst such as a base, and exhibits high reactivity for the hydroboration of alkynes under mild conditions. A gram-scale hydroboration of terminal phenylacetylene demonstrated the applicability of the copper complex for the preparation of alkenyl boronates.