Developing cost-effective electrocatalysts for both oxygen evolution reaction (OER) and hydrogen evolution reaction (HER) in basic media is critical to renewable energy conversion technologies. Here, we report a ternary hybrid that is constructed by in situ growth of cobalt selenide (Co_0.85Se) nanosheets vertically oriented on electrochemically exfoliated graphene foil, with subsequent deposition of NiFe layered-double-hydroxide by a hydrothermal treatment. The resulting 3D hierarchical hybrid, possessing a high surface area of 156 m² g^-1 and strong coupling effect, exhibits excellent catalytic activity for OER, which only requires overpotentials of 1.50 and 1.51 V to attain current densities of 150 and 250 mA cm^-2, respectively. These overpotentials are much lower than those reported for other non-noble-metal materials and Ir/C catalysts. The hybrid also efficiently catalyzes HER in base with a current density of 10 mA cm^-2 at an overpotential of -0.26 V. Most importantly, we achieve a current density of 20 mA cm^-2 at 1.71 V by using the 3D hybrid as both a cathode and an anode for overall water splitting, which is well comparable to the integrated performance of Pt/C and Ir/C catalysts.