We study the γ-ray emission from an outer-gap accelerator around a rotating neutron star. Assuming the existence of global currents in the magnetosphere, the charge depletion causes a large electric field along the magnetic field lines. This electric field accelerates migratory electrons and positrons which radiate gamma-rays via curvature radiation. These gamma-rays, in turn, produce yet more radiating particles by colliding with the X-rays, leading to a pair-production cascade. Imposing a gap-closure condition that a single pair produces one pair in the gap, on average, we explicitly solve the strength of the acceleration field and demonstrate how the peak energy and the luminosity of the curvature-radiated GeV photons and the cutoff energy and luminosity of Compton-scattered TeV photons depend on such parameters as the surface temperature, the rotational frequency, and the magnetic moment. It is demonstrated that both the GeV and TeV emissions of Geminga will be harder than those of B1055-52, B0656+14, and Vela, and that the TeV fluxes are too small to be observed by current ground-based telescopes.