Selective hydrogenation of a polyunsaturated hydrocarbon feed containing at least 2 carbon atoms per molecule and having an end point of 250° C. or less, by contacting said feed with a catalyst having an active phase of at least one metal from group VIII deposited on a support formed by at least one oxide, said catalyst being prepared using a process involving at least: i) contacting said support with at least one solution containing at least one precursor of metal from group VIII; ii) contacting said support with at least one organic compound formed from at least one cyclic oligosaccharide composed of at least 6 α-(1,4)-bonded glucopyranose subunits; iii) calcining to obtain metal from group VIII in oxide form; i) and ii) possibly being carried out separately, in any order, or simultaneously.