The hydroamination reaction of alkynes has been widely studied, but has not been developed as a powerful tool for polymer synthesis. Herein, a novel Cu(I)-catalyzed polyhydroamination has been developed for the facile preparation of nitrogen-containing polymers. This polymerization proceeded smoothly in bulk with 100% atom utilization in a regio-specific and stereo-selective fashion, producing polyenamines with well-defined structures and high molecular weights (up to 13 470) in high yields (up to 97%). Thus, this polymerization is a kind of amino-yne click polymerization. The resulting polymers possess excellent solubility, high thermal stability, strong UV-light shielding efficiency, and good visible light transparency. Considering the high efficiency, ready monomer availability and excellent performance of the products, this Cu(I)-catalyzed amino-yne click polymerization opens up enormous opportunities for preparing functional polymers.