The invention provides a propylene polymer composition well balanced and excellent in transparency, flexibility, heat resistance, scratch resistance and rubber elasticity, and a medical tube made from the propylene polymer composition. The propylene polymer composition satisfies all the following properties (A), (B), (C) and (D): (A) the composition shows a loss tangent (tan .delta.) peak at a temperature in the range of -20 to 25.degree. C. according to dynamic viscoelasticity measurement (10 rad/s) in a torsion mode, and the peak is 0.5 or above; (B) the storage elastic modulus G' at 20.degree. C. from the dynamic viscoelasticity measurement is in the range of 1.0.times.10.sup.7 to 4.9.times.10.sup.8 dyn/cm.sup.2; (C) the penetration temperature (.degree. C.) determined in accordance with JIS K 7196 is in the range of 60 to 160.degree. C.; and (D) the composition has a permanent set of not more than 30% as determined after the composition fixed between chucks 30 mm apart is 100% strained at a stress rate of 30 mm/min, maintained for 10 minutes and released for 10 minutes. The medical tube is made from the propylene polymer composition.