There remain major challenges in using density functional theory (DFT) to accurately predict some important chemical properties such as ionization potential (IP), electron affinity (EA) and their difference (i.e. fundamental band gap, Eg = IP – EA). The main problem of relating Kohn-Sham (KS) frontier orbital energies to these properties have been traced to the delocalization errors by Yang and co-workers, because common approximate functionals exhibit a convex behaviour in violation of the exact linearity condition for fractional charges. It is not clear, however, how a new class of approximate functionals, namely doubly hybrid (DH) functionals, behaves in this situation. We present here such an analysis and show that the XYG3 type of DH functionals [2,3] give good agreement between the frontier orbital energies and the experimental IP, EA, and Eg, as expected from their nearly straight line fractional charge behaviors.