Quaternized poly(2,6-dimethylphenylene oxide) materials (PPOs) containing clicked 1,2,3-triazoles were first prepared through CuI-catalyzed “click chemistry” to improve the anion transport in anion-exchange membranes (AEMs). Clicked 1,2,3-triazoles incorporated into AEMs provided more sites to form efficient and continuous hydrogen-bond networks between the water/hydroxide and the triazole for anion transport. Higher water uptake was observed for these triazole membranes. Thus, the membranes showed an impressive enhancement of the hydroxide diffusion coefficient and, therefore, the anion conductivities. The recorded hydroxide conductivity was 27.8–62 mS cm−1 at 20 °C in water, which was several times higher than that of a typical PPO-based AEM (TMA-20) derived from trimethylamine (5 mS cm−1). Even at reduced relative humidity, the clicked membrane showed superior conductivity to a trimethylamine-based membrane. Moreover, similar alkaline stabilities at 80 °C in 1 M NaOH were observed for the clicked and non-clicked membranes. The performance of a H2/O2 single cell assembled with a clicked AEM was much improved compared to that of a non-clicked TMA-20 membrane. The peak power density achieved for an alkaline fuel cell with the synthesized membrane 1a(20) was 188.7 mW cm−2 at 50 °C. These results indicated that clicked AEM could be a viable strategy for improving the performance of alkaline fuel cells.