In the hydroconversion processes of heavy hydrocarbon oils, in which the hydrogen is introduced at the reactor base by bubbling, the low diffusion rate of hydrogen, from the gas phase to the reaction liquid, limits the degree of conversion. The process circumvents the obstacle of the limited amount of reactant hydrogen by using a slurry bubble column reactor which reduces the formation of light hydrocarbon products, and therefore the hydrogen required for the hydroconversion, allowing to operate at full conversion.