Exploring highly active and durable Earth-abundant electrocatalysts to replace the precious noble metals holds great promise for the hydrogen evolution reaction (HER) from water splitting. Herein, a novel (110) high-index faceted binary-metal selenide (FeNiSe) nanosheet array grown on electrochemically exfoliated graphene foil (FeNiSe-NS/EG) is developed from its vertically-oriented NiFe-LDH nanosheet/EG precursor through a low-temperature selenization reaction. Benefiting from its unique 3D configuration and enhanced electrical conductivity, the obtained FeNiSe-NS/EG electrode exhibits excellent electrocatalytic activity toward the HER with small overpotentials of -187 and -222 mV at current densities of 10 and 20 mA cm-2, a low Tafel slope of 65 mV dec-1, and remarkable long term stability in alkaline media, outperforming the recently reported NiFe-based non-precious metal HER catalysts. Theoretical calculations and experimental results reveal that the synergistic effects of the exposed (110) high-index facets and Fe dopants give rise to a greatly enhanced HER performance.