The size distribution of free-volume (<~0.1 nm3) of ethylene-vinyl alcohol copolymer with various crystalline degrees was estimated by positronium lifetime measurement. With increasing degree of crystallinity, the size distribution significantly narrowed and the intensity of positronium decreased. This indicates that the inhomogeneity reduces with the increase of the degree of crystallinity. It is found that the free-volume fraction estimated is reflected by the fraction of the amorphous region.