A process for the synthesis of linear paraffinic hydrocarbons from a feed comprising carbon monoxide and dihydrogen in the presence of a mesoporous oxide matrix and cobalt prepared by mixing, at least one molecular precursor of cobalt and at least one colloidal precursor of mesoporous oxide matrix and by silicon, aluminium, titanium, zirconium, cerium or mixtures thereof, dissolved in aqueous or hydro-organic solvent; spray drying the mixture obtained to form spherical liquid droplets; drying the droplets to obtain solid particles activating the solid particles by reduction to form nanoparticles of cobalt with an oxidation state of 0.