There is provided a vinyl alcohol-based polymer having an ethylenic double bond with a saponification degree of 70 mol % or more, wherein the vinyl alcohol-based polymer is water-soluble; a molar ratio of the ethylenic double bond to the total of vinyl alcohol units and vinyl acetate units is 0.05/100 to 2/100; and a limiting viscosity [η] and a weight-average molecular weight Mw of a vinyl ester-based polymer which is produced by esterifying the vinyl alcohol-based polymer satisfy the following formulas (1) and (2). 4.7≤log Mw 6.3  (1) 0.60