A method for producing acetic anhydride and acetic acid by reacting methanol and methyl acetate and optional methyl ether with carbon monoxide, the method comprises the following steps: (a) in the presence of catalyst in the reaction zone, methanol and methyl acetate are mixed at 150-250 ℃ and 5-120 bar Selectively reacting with carbon monoxide or a mixture of carbon monoxide and hydrogen together with methyl ether（ b) Under the pressure from 5 bar to higher than atmospheric pressure, the carbonylation mixture discharged from the reaction zone is flash evaporated in the vapor-liquid separation zone, and the main volatile fraction is evaporated and sent to the distillation zone, and then the non evaporated catalyst solution in the vapor-liquid separation zone is recycled to the reaction zone（ c) In the distillation zone, the low boiling fraction is obtained from the top of the column and recycled to the reaction zone. At the same time, the high boiling fraction containing the catalyst mixed from the bottom of the column is obtained and recycled to the reaction zone and / or the vapor-liquid separation zone. As the side fraction, the middle boiling fraction mainly containing acetic acid or acetic anhydride is obtained（ d) The distillation zone is used as the side fraction, and the main middle boiling point fraction containing acetic acid and acetic anhydride is sent to the second distillation zone（ e) The remaining low boiling fraction from the top of the column is further obtained in the second distillation zone and recycled to the reaction zone（ f) A fraction consisting mainly of a side fraction or of acetic anhydride and acetic acid from the bottom of a distillation column is obtained and fed to a third distillation zone, or a high boiling fraction containing a portion of a catalyst, for example, entrained and mixed by the bottom of a distillation column, is obtained and recycled to a reaction zone and / or a vapor-liquid separation zone, At the same time, the side fraction of the fraction mainly composed of acetic anhydride and acetic acid is obtained and sent to the third distillation zone; And (g) obtaining acetic acid from the top of the column as a side fraction or acetic anhydride from the bottom of the column in the third distillation zone.