An ultraviolet-crosslinkable polymer composition comprising a polymer containing iodine and/or bromine in an amount of from 0.001 to 10% by weight, a photoinitiator as a crosslinking agent and a polyfunctional unsaturated compound as a crosslinking aid. By using iodine and/or bromine as a crosslinking point, it is possible to carry out crosslinking of various polymers including fluorine-containing polymers which have been very difficult to crosslink with ultraviolet rays, and molding or processing can be made easily at working site at low temperature.