NOVELTY - The process comprises forming a feedstock by combining a hydrocarbon fuel containing renewable organic material with a hydrogen stream (2), conducting the formed feedstock to a hydrotreating stage by contacting the feedstock with a fixed bed of hydrotreating catalyst, passing an effluent (4) from one of the catalyst fixed beds to a hot separator (13) and withdrawing from the hot separator to an overhead fraction and a bottom fraction (5), passing the overhead fraction to a water gas sour-shift stage, and passing the effluent from one of the catalyst fixed beds to a cold separator (16).    USE - The process is useful for hydrotreating including hydrodesulfurization and/or hydrodenitrogenation of a hydrocarbon fuel (claimed) with co-production of hydrogen.    ADVANTAGE - The process ensures simple, economic and safe hydrotreatment of the hydrocarbon fuel with reduced need of hydrogen and water in the hydrotreating stage and without hazardous solutions, injection of oxygen from an external source and producing impurities such as sulfur and nitrogen.    DETAILED DESCRIPTION - The process comprises forming a feedstock by combining a hydrocarbon fuel containing renewable organic material with a hydrogen stream (2), conducting the formed feedstock to a hydrotreating stage by contacting the feedstock with a fixed bed of hydrotreating catalyst, passing an effluent (4) from one of the catalyst fixed beds to a hot separator (13) and withdrawing from the hot separator to an overhead fraction and a bottom fraction (5), passing the overhead fraction to a water gas sour-shift stage, passing the effluent from one of the catalyst fixed beds to a cold separator (16) and withdrawing from the cold separator to a gaseous overhead fraction in the form of a hydrogen-rich recycle gas stream, passing the gaseous overhead fraction to a hydrogen sulfide recovery unit in which a solvent is contacted with the gaseous stream, withdrawing from the recovery unit to a gaseous stream with reduced content of hydrogen sulfide and carbon dioxide and withdrawing from the recovery unit to a solvent containing hydrogen sulfide and carbon dioxide, returning the gaseous stream with reduced content of hydrogen sulfide and carbon dioxide or returning the gaseous stream with reduced content of hydrogen sulfide and carbon dioxide by dividing the gaseous stream into two streams and returning one of these streams to the forming a feedstock and one of these streams to the passage of the overhead fraction. The hydrogen stream is a hydrogen-recycle gas stream and/or a hydrogen make-up gas. The content of the renewable organic material in the hydrocarbon fuel is 5 vol.%. The water gas sour-shift stage is lower water gas shift, medium water gas shift and/or high water gas shift. Steam is added to the overhead fraction of the gaseous stream with reduced content of hydrogen sulfide and carbon dioxide before conducting the water gas sour-shift stage. Water (0.1-10 wt.%) of the hydrocarbon fuel is added to the feedstock and/or to the fixed beds of hydrotreating catalyst.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a process for hydrotreating of a hydrocarbon fuel.    Hydrogen stream (2)    Effluent (4)    Bottom fraction (5)    Hot separator (13)    Cold separator. (16)