The invention discloses a methyl formate continuous esterification method and device. The method comprises the following steps of taking methyl alcohol and formic acid as the raw materials to perform esterification reaction in a first high-pass microchannel reactor, continuously feeding obtained reactants into a first vapor-liquid separator, feeding separated gas phase into the upper section of a dehydrating tower, and feeding separated liquid phase into a second high-pass microchannel reactor; continuously feeding methyl alcohol into the second high-pass microchannel reactor for esterification reaction, continuously feeding obtained reactants into a second vapor-liquid separator, feeding separated gas phase into the upper section of the dehydrating tower, and feeding separated liquid phase into the lower section of the dehydrating tower; discharging materials from the top of the dehydrating tower and into an alcohol-ester separating tower, and controlling the reflux ratio so that the content of methyl ester at the top of the alcohol-ester separating tower can be higher than 97%. The methyl formate continuous esterification method achieves continuous reaction of methyl formate, and through the high-pass microchannel reactors, increases the reaction temperature and the reaction efficiency, reduces side reactions and achieves a synthesizing rate up to higher than 98%.