The invention relates to a catalyst which can be applied to a method for converting synthesis gas, said catalyst comprising: a) a support made of a solid solution containing at least one first aluminate element with a mixed spinel structure of formula MxM′(1-X)AI2O4/AI203.SiO2, x ranging from 0 to 1 being excluded, or a simple spinel structure of formula MAI2O4/AI2O3 SiO2, wherein the support is calcinated in an at least partially oxidizing atmosphere at a temperature ranging from 850° C. to 900° C., b) an active phase which is deposited on the support which contains one or several metals of group VIII, selected from amongst cobalt, nickel, ruthenium or iron. The catalyst is used in a fixed bed or in a suspension in a triphasic reactor for the synthesis of hydrocarbons from a CO, H2 mixture.