TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The mineral oil (2) is pressurized in a pump (201), heated by thermal exchange in heat exchangers (204, 203) and sent by a line (103). The oil or natural fat (1) is pressurized in a pump (202) to obtain a flow (105). The mineral oil flow (103) is mixed with the oil or natural fat flow (105) to obtain a flow (106), which is then mixed with hydrogen-rich recycle gas flow (119), from which flow (107) is originated. The flow (107) is heated in a furnace (205) to the inlet temperature of a reactor (206) to form a further flow (108). Hydroconversion reaction occurs in the reactor (206) in the presence of a sulfide catalyst of VI and VIII group element, under a pressure of 4-10 MPa, a catalytic bed average temperature of 320-400degreesC, a spatial velocity of 0.5-2 per hours, and a hydrogen load ratio of 200-1000 NI of hydrogen/load, with exothermic reactions which raises the temperature along the catalytic bed. The product is separated from the reactor outlet at a temperature higher than the inlet temperature, and flow (109), which is cooled for condensation of the formed light products separated from the gas flow (113) in a vessel (208), in which a flow (111) of produced water is also separated and sent to the refinery's sour water system (3) for treatment, is separated. The hydrocarbon flow (112) containing the product is separated from vegetable oil hydrocracking, and supplied for rectification. The specified diesel (4) is recovered.Preferred Oil: The vegetable oil is castor, soya, rape seed, peanut, palm and babassu oils, or their mixture, preferably castor oil, used soya oil, animal fat, or mixture of vegetable oil and animal fat. The vegetable oil is mineral oil, which is heavy diesel, light diesel or mixture of flows such as light cycle oil (LCO) and/or coking process gasoil. The vegetable oil is chosen based on desired IQT/derived cetane number (DCN) value or density of final product.Preferred Method: The hydroconversion is carried out by substitution of glycerine production, and transesterification processes for propane production, incorporated in liquefied gas flow. A liter of diesel oil is produced for each liter of processed vegetable oil.Preferred Composition: The amount of vegetable oil or animal fat is 1-75 mass% with respect to petroleum oil.