PURPOSE: To allow only selective hydrogenation of highly unsaturated hydrocarbon to proceed by supplying hydrogen gas in portions along a passage in a fixed-bed reactor to lowly unsaturated hydrocarbon contg. the highly unsaturated hydrocarbon.

CONSTITUTION: In selective hydrogenation of highly unsaturated hydrocarbon by contacting a hydrocarbon mixt. consisting of 5C or higher lowly unsaturated hydrocarbon and contg. highly unsaturated hydrocarbon with hydrogen in the presence of a catalyst using a fixed-bed reactor, the hydrogen is supplied in portions at different points along a passage in the reactor. As the number of the portions increases, a better reaction result is obtd. but the process becomes more complicated and the operation becomes more intricate while the reaction effect is reduced, so that it is pref. to supply hydrogen in portions at 2W3 points. A pref. amt. of hydrogen gas supplied at each point is 5W100% of that of the gas supplied at a just preceding point.