The present invention relates to a process for producing a buten-1-based polymer satisfying the following requirements (a), (b) and (c): (a) a crystalline resin having a melting point (Tm-D) of 0 to 100° C., the melting point being defined as a top of a peak observed on a highest-temperature side in a melting endothermic curve obtained by a differential scanning calorimeter (DSC) when a sample is held in a nitrogen atmosphere at −10° C. for 5 min and then heated at a temperature rise rate of 10° C./min; (b) a stereoregularity index represented by (mmmm)/(mmrr+rmmr) of 20 or less; and (c) a weight-average molecular weight (Mw) of 10,000 to 1,000,000 and a ratio (Mw/Mn) of weight-average molecular weight to number-average molecular weight of 4.0 or less; a modified buten-1-based polymer produced by modifying the buten-1-based polymer with a radical polymerization initiator and an organic acid; and an adhesive composition containing the modified buten-1-based polymer. The modified buten-1-based polymer of the present invention is capable of imparting a high adhesiveness, a high strength and a good softness to polyolefins, and providing sealants having a high adhesiveness, or polyolefins having an improved compatibility to inorganic fillers, etc., in particular, is useful as resins for hot-melt adhesives.