We propose a new scheme to construct an orbital-specific (OS) hybrid functional so as to satisfy the linearity condition that the second derivative of the total energy with respect to the occupation number in Kohn-Sham density functional theory (KS-DFT) is zero. Numerical assessment confirms that the orbital energies exhibit a significantly small fractional-occupation-number dependence for NH3 molecule. The newly proposed OS hybrid functional accurately reproduces ionization potentials (IPs) of core and valence orbitals for molecules containing second and third row atoms in the sense of Koopmans’ theorem.