PURPOSE: To easily perform a highly precise hydrogenation desulfurization by use of a small device at low cost without requiring sulfiding treatment by contacting hydrocarbon fluid having a low sulfur content with a noble metal supported catalyst composition.

CONSTITUTION: Hydrocarbon fluid having a low sulfur content is preheated preferably to about 300-650° F, and contacted with a catalyst composition having platinum, palladium, rhodium or a mixture thereof on a support body preferably consisting of a (lanthanum-stabilized) alumina granular matter, and the resulting fluid is then contacted with a hydrogen sulfide absorber, whereby a highly precise desulfurization is performed.