In this paper, a physics-based compact model is developed for novel MgZnO/ZnO high-electron-mobility transistor (HEMT). Poisson’s equation coupled with 1D Schrödinger equation is solved self-consistently in the triangular quantum well to derive an expression of two-dimensional electron gas (2DEG) density with respect to gate voltage at the heterointerface of barrier (MgZnO) and buffer (ZnO) layers. A compact mathematical framework has been devised further for the first time for ZnO-based HEMT to the best of our knowledge using the expression of 2DEG density to compute surface potential, gate charge, gate current, gate capacitance, current–voltage characteristics, output conductance, transconductance and cut-off frequency with respect to gate voltage and along with the drain–source output resistance [Formula: see text].