We present a study of associated ηc and γ double diffractive production in p-p collision based on Ingelman-Schlein model, and the framework of non-relativistic QCD factorization formalism for quarkonia production. The predic-tion of ηc and γ is more reliable than J/ψ production, because the associated ηc and γ production is a pure color-octetprocess, and the dominant contribution comes from color octet 1So(8) subprocess, which is related to the color octet matrixelement of 1So(8) of J/ψ by the heavy quark spin symmetry and the large PT J/ψ production data. We find that the ratioof diffractive to inclusive cross sections is independent of the values of color octet matrix elements, but is sensitive to thegluon factor of the Pomeron and renormalized Pomeron flux factors. So experimental measurement of this ratio can giveus more information of the nature of Pomeron and test the assumption of hard diffractive factorization in hadron-hadron collisions.