An epoxidized acetylene-conjugated diene random copolymer, of which epoxy equivalent is within the range of from 50 to 1,000, is obtained by epoxidizing an acetylene-conjugated diene random copolymer, in which acetylene and conjugated diene are bonded linearly and randomly, the block character P is within the range of from 0.8 to 1.2 and the acetylene content is less than 60 mol%, with an organic peracid. The epoxidized acetylene-conjugated diene random copolymer is more reactive than the crude random copolymer and yields an excellent film, a coating material or a shaped article. Further by adding some of curing agents to the epoxidized acetylene-conjugated diene random copolymer, the cure rate of the epoxidized copolymer is fairly enhanced.