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. The intrinsic viscosity [eta] as measured in tetralin solvent at 135°C is 0.01 to 0.5 dL/g. The polymer is a crystalline resin having a melting point (Tm-D) of 0 to 100 °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°C for 5 minutes and then heated at a rate of 10 °C/min. 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%.