A polymer composition includes (1) a crystalline norbornene-based polymer and (2) an amorphous alicyclic structure-containing polymer in a weight ratio of 90:10 to 50:50, the crystalline norbornene-based polymer (1) having a melting point of 110 to 145° C., an Mw measured by gel permeation chromatography of 50,000 to 200,000, and a ratio Mw/Mn of 1.5 to 10.0, and obtained by ring-opening polymerization of a polymerizable monomer mixture (1) containing 90 to 100 wt % of 2-norbornene and 0 to 10 wt % of a substituent-containing norbornene monomer, and hydrogenating the resulting polymer, and the amorphous alicyclic structure-containing polymer (2) having a Tg of 50° C. or more and not having a melting point, and obtained by polymerization of a polymerizable monomer mixture (2) containing a 2-norbornene compound and a dicyclopentadiene compound in an amount of 50 wt % or more and less than 90 wt % in total. A film obtained by molding the polymer composition has a steam permeability of 0.40 g/m2·day or less and a haze value of 20% or less when the film has a thickness of 100 μm. A medical container is obtained by molding the polymer composition.