The invention concerns a method for purifying water in order to remove therefrom, at least one organic substance, in particular malodorous pollutants such as (-)geosmine and (+)2-methyl-isoborneol. This method consists in: contacting the water to be purified with a cyclodextrin of formula (I) in which R represents a hydrogen atom, a C1-C12 alkyl group or the CH3CO- acetyl group, R and R which can be identical or different, represent H or R , and n = 5, 6 or 7; for including therein the organic substance(s) to be removed, and in separating the water from the cyclodextrin.