NOVELTY - The content of free fatty acid in the waste oil mixture is measured. When free fatty acid content is 30 wt.% or more, the waste oil mixture is subjected to esterification reaction (a). When free fatty acid content is 16-30 wt.%, the waste oil mixture is subjected to esterification reaction (b). When free fatty acid content is 5-16 wt.%, the waste oil mixture is subjected to esterification reaction (c). The esterification (a) reaction is carried out by mixing waste oil mixture with methanol solution (m6) and separating methanol solution (m7) from waste oil reactant.    USE - Production of fatty acid methyl ester used for biodiesel.    ADVANTAGE - The method enables economical production of fatty acid methyl ester, with high yield.    DETAILED DESCRIPTION - The content of free fatty acid in waste oil mixture containing free fatty acid is measured. When free fatty acid content is 30 wt.% or more, the waste oil mixture is subjected to esterification reaction (a). When free fatty acid content is 16-30 wt.%, the waste oil mixture is subjected to esterification reaction (b). When free fatty acid content is 5-16 wt.%, the waste oil mixture is subjected to esterification reaction (c). The esterification (a) reaction is carried out by mixing waste oil mixture with methanol solution (m6) to obtain waste oil reactant, separating methanol solution (m7) from waste oil reactant to obtain waste oil reactant, and measuring free fatty acid content of waste oil mixture, when free fatty acid content is 30 wt.% or more, carrying out esterification reaction (a), and when free fatty acid content is 16-30 wt.%, carrying out esterification reaction (b). The esterification reaction (b) is carried out by mixing waste oil mixture with methanol solution (m1) to obtain waste oil reactant, separating methanol solution (m2) from waste oil reactant to obtain waste oil reactant and measuring content of free fatty acid in waste oil reactant, when content of free fatty acid is 16-30 wt.%, carrying out esterification reaction (b) and when content of free fatty acid is 5-16 wt.%, carrying out esterification reaction (c). The esterification reaction (c) is carried out by mixing waste oil reactant with methanol solution (m3) containing sulfuric acid to obtain waste oil mixture, the content of sulfuric acid is 5-25 wt.%, separating methanol solution (m4) containing sulfuric acid and waste oil mixture from waste oil reactant, and measuring content of free fatty acid in waste oil reactant, when content of free fatty acid is 5-16 wt.%, carrying out esterification reaction (c), and when content of free fatty acid is 0-5 wt.%, carrying out transesterification reaction (t1). The transesterification reaction (t1) is carried out by reacting waste oil reactant with catalyst (c2), adding catalyst (c1) and methanol solution (m5) to waste oil reactant, and separating glycerol and fatty acid methyl ester from waste oil reactant. The water content of methanol solution (m1), methanol solution (m2) and methanol solution (m4) is 0.3 wt.% or more. The water content of methanol solution (m3) and methanol solution (m5) is 0.3 wt.% or less. The molar ratio of methanol solution (m3) and free fatty acid of waste oil reactant is 22:1-200:1.