Anion exchange membranes (AEMs) are crucial materials in hydrogen production techniques via water electrolysis. Whereas, the "trade-off" between the conductivity and dimensional stability of AEMs, as well as poor alkaline stability, hinders the advancement of AEMs and water electrolysis technologies. Cross-linking serves as a pivotal strategy for addressing the "trade-off" effect, thereby facilitating the fabrication of highly conductive and durable AEMs. In this study, a series of poly (carbazole)-based AEMs, designated as QPBHC-x, were synthesized utilizing the flexible cross-linker N,N,N ',N '-tetramethyl-1,6-hexanediamine (TMHDA). The synthesized AEMs demonstrated reduced water uptake and enhanced alkaline stability in comparison to uncross-linked AEMs, while maintaining a conductivity retention exceeding 92 % after immersion in 1 M NaOH solution at 80 degrees C for 720 h. AFM and SAXS analyses revealed the microphase separation structure in the prepared AEMs, which construct continuous ion channels and promote ion conduction. Specifically, the QPBHC-0.5 demonstrated a conductivity of 102.3 mS cm- 1 at 80 degrees C and exhibited a tensile strength of 46.6 MPa. Furthermore, anion exchange membrane water electrolysis (AEMWE) single cell (cathode: Pt/C and anode: NiFe2O4) based on QPBHC0.75 achieved a current density of 1.40 A cm- 1 at 2 V in 1 M KOH (80 degrees C). Meanwhile, QPBHC-0.5 maintained stable operation for over 470 h at 1.0 A cm- 1 in 1 M KOH (80 degrees C) with a voltage decay rate of 352 mu V h-1. These results indicate promising applications of cross-linked poly (carbazole)-based AEMs in water electrolysis.