The invention relates to a supported copper-base catalyst for alkyne selective hydrogenation. The catalyst comprises a carrier and following components loaded on the carrier: (a) 5 to 15 wt% of copper, (b) 0.5 to 3 wt% of iridium, (c) 0.5 to 3 wt% of phosphor, and optional zirconium and/nickel. The carrier is preferably chosen from aluminum oxide, titanium oxide, silicon oxide, titanium oxide-aluminum oxide, titanium oxide-silicon oxide, or aluminum oxide-silicon oxide, and most preferably, the carrier is titanium oxide-aluminum oxide. The catalyst can be used to eliminate alkyne in C4 fraction through hydrogenation, has the advantages of high catalytic activity, high selectivity, good stability, and long service life, and is capable of preventing sulfur and arsenic poisoning.