A vegetable oil hydroconversion process is described for hydroconverting a mixture between 1 to 75% in mass of oil or natural fat (1) and the rest mineral oil (2), hydroconverted in a reactor (205) under conditions of pressure, temperature, hydrogen (flow 119) and sulfide catalyst of Groups VIII and VIB, obtaining, after sour water separation (flow 111) and rectification (flow 112), a specified diesel product (4). The product (4) has an ITQ/DCN (cetane number) higher than a product obtained from a pure mineral based oil would have, lower density than from a base oil and a plugging point depending on the mineral oil flow, as well as greater oxidation stability than the base oil.