Quark-hadron duality refers to an assumption that one can use perturbative QCD to compute a class of physical processes. Its associated uncertainty is hard to quantify, and even ignored in some cases, which may pose significant problem on the analysis of precise experimental data. We develop a formalism to get rid of this assumption and compute the physical processes fully non-perturbatively using lattice QCD. Examples are inclusive semileptonic decays of B meson and lepton-nucleon inelastic scattering cross section at low energy.