A Cu-catalyzed highly Z-stereoselective hydroboration of alkynes with 1,8-naphthalenediaminatoborane (HB(dan)) is developed. DPEphos (bis[(2-diphenylphosphino)phenyl]ether)-ligated Cu catalysts produced alkenylboron compounds from terminal alkynes with excellent Z-stereoselectivity. In contrast, using a SIPr-CuCl complex as the precatalyst exclusively produced E-hydroboration products at mild conditions. Both catalytic procedures form alkenylboron products stereocomplementary to each other, constituting stereodivergent hydroboration of alkynes through Cu catalysis. Deuterium labeling and isomerization studies support the Z-selective hydroboration via trans-addition of the boron reagent to terminal alkynes as opposed to precedent noble-metal-catalyzed trans-hydroborations.