An object of the present invention is to provide a modified vinyl alcohol polymer having a sulfonic acid or a salt thereof, the polymer having notably improved water solubility as compared with a pre-modified vinyl alcohol polymer. A modified vinyl alcohol polymer (A) has in a side chain thereof a sulfonic acid group or a salt thereof, and in the modified vinyl alcohol polymer (A), a degree of modification with the sulfonic acid group or the salt thereof is 0.01 mol % or more and 10 mol % or less, and a block character of residual vinyl ester units is 0.55 or more and 1 or less.