We report a photodetachment photoelectron spectroscopy study of a doubly charged anion, ZrF62-, in the gas phase at two photon energies: 6.424 (193 nm) and 7.865 (157 nm) eV. The adiabatic detachment energy, i.e., the second electron affinity of ZrF6, was measured to be extremely high, 2.9(0.2) eV. The vertical detachment energy (VDE) was measured to be 3.4(0.1) eV. Two excited states were also observed for the ZrF6- singly charged anion with VDEs at 4.0 and 4.6 eV, respectively. The repulsive Coulomb barrier and hence the intramolecular Coulomb repulsion in ZrF62-, was estimated from the photon-energy-dependent spectra to be similar to 2.4 eV. The ZrF62- dianion was observed to be metastable with a half-life of similar to 4 s under our experimental conditions, confirming theoretical predictions that ZrF62- is thermodynamically unstable against loss of an F-, despite its extremely high electronic stability. We also performed experiment for the singly charged ZrF5-, but could not observe photodetachment even at 157 nm, the highest photon energy available to us. Thus, we estimated that the electron affinity of ZrF5 is larger than 7.8 eV, the highest electron affinity yet confirmed experimentally.