A process for the synthesis of linear paraffinic hydrocarbons from a feed of carbon monoxide and dihydrogen in the presence of a catalyst of a mesoporous oxide matrix and a content by weight of the element cobalt of 0.5% to 60%, wherein the catalyst is prepared by a) mixing, in an aqueous or hydro-organic solvent, a molecular precursor containing cobalt and a molecular precursor of the mesoporous oxide matrix containing element X of silicon, aluminium, titanium, zirconium and or cerium; b) aerosol spray drying the mixture to form spherical liquid droplets; c) drying to obtain solid particles at a temperature of 10° C. to 300° C.; d) activation by a reduction treatment to form nanoparticles of cobalt with an oxidation state of 0.