Zinc ion hybrid capacitors suffer from lack of reversibility and dendrite formation. An electrolyte, based on a solution of a zinc salt in acetonitrile and tetramethylene sulfone, allows smooth zinc deposition with high coulombic efficiency in a Zn||stainless steel cell (99.6% for 2880 cycles at 1.0 mA cm⁻², 1.0 mAh cm⁻²). A Zn||Zn cell operates stably for at least 7940 h at 1.0 mA cm⁻² with an area capacity of 10 mAh cm⁻², or 648 h at 90% depth of discharge and 1 mA cm⁻², 9.0 mAh cm⁻². Molecular dynamics simulations reveal the reason for the excellent reversibility: The zinc cation is only weakly solvated than in pure tetramethylene sulfone with the closest atoms at 3.3 to 3.8 Å. With this electrolyte, a zinc||activated-carbon hybrid capacitor exhibits an operating voltage of 2.0 to 2.5 V, an energy-density of 135 Wh kg⁻¹ and a power-density of 613 W kg⁻¹ at 0.5 A g⁻¹. At the very high current-density of 15 A g⁻¹, 29.3 Wh kg⁻¹ and 14 250 W kg⁻¹ are achieved with 81.2% capacity retention over 9000 cycles.