In this paper, a multiscale approach coupling semi-classical drift-diffusion (DD) and the quantum mechanical non-equilibrium Green's function (NEGF) formalism is established to simulate the full geometry of miniaturized GaN high electron mobility transistors (HEMTs). DD current flow is corrected locally in the HEMT channel, where electron transport represented by the NEGF is governed by quantum effects. As a result, simulated drain current-drain voltage and drain current-gate voltage curves are easily fitted to experimental data without fitting mobility. The variation of electric behavior predicted by our multiscale approach is in agreement with that expected from 2D electrostatics. This work indicates that it is practical and efficient to include NEGF in a DD solver, which is still the workhorse of the technology computer-aided design industry.