Nontraditional polyurethane (PU) has been successfully synthesized by anionic copolymerization of some typical aryl isocyanates and epoxides with ammonium halide onium salt (Lewis base) as the initiator and triisobutylaluminum (Lewis acid) as the activator and the synergistic coordinator. In contrast to the traditional step-growth approach, this chain-growth copolymerization can maintain the anionic propagation site and exhibit some living features with a high activity, by which the copolymers synthesized have narrow molecular weight distributions and discrete end groups. The copolymer is primarily constituted by a urethane linkage, and the byproducts of isocyanurate trimer and oxazolidinone can be effectively suppressed as the polymerization proceeds. Density functional theory (DFT) calculations were also performed to support the proposed reaction mechanism.