Polycyclic N-heterocycles are important structural motifs commonly found in bioactive compounds, however, their selective construction via the cyclization of allenynes remains challenging yet highly desirable. Here we show a homogeneous copper-catalyzed hetero Diels−Alder (HDA) reaction of allenynes with cis-diazenes (PTAD, 4-phenyl-1,2,4-triazoline-3,5-dione), allowing the practical and efficient synthesis of a diverse array of valuable polycyclic N-heterocycles. A temperature-controlled and stereocontrolled chemoselectivity of the reaction was observed, leading to the chemodivergent synthesis of tetracyclic pyrrolidines, pentacyclic triazepanes and tricyclic pyrrolidines. Compared with related Au-catalyzed cyclization of allenynes, this copper catalysis achieves cyclization of allenynes terminating in C–N bond formation via the HDA reaction.