Anionic metal-organic frameworks (MOFs) are promising single-ion conductive electrolytes in quasi-solid-state batteries. Herein, we propose an anionic MOF as a promising single Zn2+ conductor for high-performance quasi-solid-state zinc-ion battery (ZIB). The anionic MOF is synthesized by reacting carboxylic acid functionalized tetraphenylborate with a Zr6-oxo cluster, which displays outstanding ionic conductivity (0.83 mS cm-1 at -40 °C, 2.75 mS cm-1 at 25 °C, and 7.9 mS cm-1 at 120 °C), an impressive Zn2+ transference number (tZn2+ = 0.90), low activation energy (0.19 eV), good interfacial compatibility, and excellent rate performance. The fabricated quasi-solid-state ZIB using NH4V4O10 cathode delivers a remarkable capacity of 497 mAh g-1 at 0.3 A g-1 under ambient conditions and can maintain capacities of 420, 350, and 270 mAh g-1 at elevated current densities of 1, 5, and 10 A g-1 with both capacities and Coulombic efficiency retention at 100% after 2500 cycles. Even at a low temperature of -40 °C or with a high current density of 100 A g-1, excellent reversible capacities and rate performance can still be achieved. This work set up a new direction for designing and developing anionic porous materials as advanced solid electrolytes for zinc and/or other secondary batteries.