A 1-butene polymer satisfying the following (1), (2) and either (3) or (3'): a process for producing the polymer; a resin modifier comprising the polymer; and a hot-melt adhesive containing the polymer. (1) The intrinsic viscosity [.eta.] as measured in tetralin solvent at 135.degree. C. is 0.01 to 0.5 dL/g. (2) The polymer is a crystalline resin having a melting point (Tm-D) of 0 to 100.degree. C., the melting point being defined as the top of the peak observed on the highest-temperature side in a melting endothermic curve obtained with a differential scanning calorimeter (DSC) in a test in which a sample is held in a nitrogen atmosphere at -10.degree. C. for 5 min and then heated at a rate of 10.degree. C./min. (3) The stereoregularity index {(mmmm)/(mmrr+rmmr)} is 30 or lower. (3') The mesopentad content (mmmm) determined from a nuclear magnetic resonance (NMR) spectrum is 68 to 73%.