A process for producing a butene-1 polymer which: (a) is a crystalline resin having a melting point (Tm-D), defined as the temperature corresponding to the top of the peak observed on the highest-temperature side in a melting endothermic curve obtained by DSC analysis in which a sample in a nitrogen atmosphere is held at -10°C for 5 minutes and then heated at a rate of 10 °C/min, of 0 to 100°C; (b) has a stereoregularity index represented by [mmmm]/([mmrr]+[rmmr]) of 20 or lower; and (c) has a weight-average molecular weight (Mw) of 10,000 to 1,000,000 and a weight-average molecular weight/number-average molecular weight ratio (Mw/Mn) of 4.0 or lower. Also provided are: a modified butene-1 polymer obtained by modifying the butene-1 polymer with a free-radical initiator and an organic acid; and an adhesive composition containing the modified butene-1 polymer. The modified butene-1 polymer can impart high adhesion, high strength, flexibility, etc. to polyolefins, etc. It gives a highly adhesive sealant or a polyolefin having improved compatibility with inorganic fillers, etc. It is especially useful as a resin for hot-melt adhesives.