We present a formulation and calculations of multiband quantum transport of electrons in resonant tunneling diodes (RTDs) based on a non-equilibrium Green function theory. In the formulation we have used an empirical tight-binding method to include a realistic band structure, where evanescent-wave matching at heterointerfaces, Gamma -X valley-mixing effects, and space charge effect are duly taken into account. Our results show that the current-voltage characteristics of a GaAs/AlAs double-barrier RTD has a larger current density than the conventional single band (SB) model since the latter is found to overestimate the decay constant in the barriers. Note that matching of evanescent electron modes essentially requires the inclusion of valley-mixing effects for GaAs/AlAs heterostructures owing to breaking of lattice-translational symmetry occurring at interfaces.