We present a density functional theory-based method for calculating thermionic emission currents from a cathode into vacuum using a non-equilibrium Green's function approach. It does not require semi-classical approximations or crude simplifications of the electronic structure used in previous methods and thus provides quantitative predictions of thermionic emission for adsorbate-coated surfaces. The obtained results match well with experimental measurements of temperature-dependent current densities. Our approach can thus enable computational design of composite electrode materials.