A process for hydrodeoxygenation of feeds derived from renewable sources with conversion by decarboxylation/decarbonylation limited to at most 10%, using a bulk or supported catalyst comprising an active phase constituted by at least one element from group VIB and at least one element from group VIII, said elements being in the sulphide form, and the atomic ratio of the metal (or metals) from group VIII to the metal (or metals) from group VIB being strictly more than 0 and less than 0.095, said process being carried out at a temperature in the range 120° C. to 450° C., at a pressure in the range 1 MPa to 10 MPa, at an hourly space velocity in the range 0.1 h−1 to 10 h−1, and in the presence of a total quantity of hydrogen mixed with the feed such that the hydrogen/feed ratio is in the range 50 to 3000 Nm3 of hydrogen/m3 of feed.