The invention discloses a continuous dehydration esterification reaction device as well as a continuous esterification reaction method, belonging to the technical field of esterification reaction. A membrane reactor comprises a vertically fixed cylindrical housing (12) and a plurality of tubular molecule sieve membranes (13) axially fixed in the housing (12), wherein a fixed bed catalyst (14) is filled in the tubular molecular sieve membranes (13); the charging hole (18) of the membrane reactor is arranged at the lower end of the housing (12) and communicated with a material mixing and preheating device; the discharging hole (11) of the membrane reactor is arranged at the upper end of the housing (12) and communicated with a storage tank (33). The continuous esterification reaction method comprises the following steps of: mixing and adding alcohol and oleic acid in a molar ratio of 1:1-12:1 into the material mixing and preheating device, heating up to 75 DEG C-85 DEG C and feeding to the membrane reactor; reacting alcohol and oleic acid under catalytic action of the fixed bed catalyst (14), extracting water generated in the reaction by a dehydrating device to promote the reaction to be carried out toward a positive direction, and storing reaction products in the storage tank (33) through the discharging hole (11) of the membrane reactor.