NOVELTY - Producing biodiesel by transesterification reaction of oil and fat with alcohol, comprises e.g.: (a) introducing oil and fat and alcohol dissolved with a metal precursor into a reactor, (b) synthesizing metal oxide of metal precursor dissolved in alcohol via solvothermal reaction inside the reactor, and simultaneously performing transesterification reaction of oil and fat with alcohol by using synthesized metal oxide as catalyst, and (c) obtaining biodiesel by separating biodiesel, metal oxide and glycerol formed via the transesterification reaction and solvothermal reaction.    USE - The method is useful for producing biodiesel by transesterification reaction of oil and fat with alcohol (claimed).    ADVANTAGE - The method: synthesizes metal oxide which acts as catalyst in the transesterification reaction of alcohol having supercritical or subcritical state with oil and fat, where the yield of fatty acid alkyl ester in the biodiesel is 60-99% (claimed); and is economical, and ensures improved yield of biodiesel by using economical metal precursor.    DETAILED DESCRIPTION - Producing biodiesel by transesterification reaction of oil and fat with alcohol, comprises either: (a) introducing oil and fat and alcohol dissolved with a metal precursor into a reactor, (b) synthesizing metal oxide of metal precursor dissolved in alcohol via solvothermal reaction inside the reactor, and simultaneously performing transesterification reaction of oil and fat with alcohol by using synthesized metal oxide as catalyst, and (c) obtaining biodiesel by separating biodiesel, metal oxide and glycerol formed via the transesterification reaction and solvothermal reaction; or (i) dissolving (S110) metal precursor in alcohol, (ii) introducing (S120) preheated oil and fat with alcohol dissolved with metal precursor into the reactor, (iii) synthesizing (S130) metal oxide of metal precursor dissolved in alcohol having supercritical or subcritical state via solvothermal reaction inside the reactor, (iv) synthesizing (S140) biodiesel and glycerol by promoting transesterification reaction of alcohol with oil and fat by using the synthesized metal oxide as catalyst within the reactor, (v) filtering the reaction solution to separate the synthesized metal oxide after completion of the transesterification reaction, and (vi) separating (S150) biodiesel and glycerol respectively.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic process flow for producing biodiesel by transesterification reaction of oil and fat with alcohol (Drawing includes non-English language text).    Metal precursor dissolving step (S110)    Oil and fat and alcohol introducing step (S120)    Metal oxide synthesizing step (S130)    Biodiesel and glycerol synthesizing step (S140)    Biodiesel separating step (150)