This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: ∂(2)E/∂f(i)(2)|(0≤f(i)≤1) = ∂ɛ(i)/∂f(i)|(0≤f(i)≤1) = 0, where E, ε(i), and f(i) represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree-Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans' theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core-valence-Rydberg-Becke-3-parameter-Lee-Yang-Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)].