An accurate physical model for GaN high-electron-mobility-transistors (HEMTs) device is imperative and crucial for circuit design and technology optimization. In this paper, a scalable large-signal surface-potential (SP) model of AlGaN/GaN HEMTs is presented. The drain current model is capable of accurately modeling the self-heating effect and trapping effect. The self-heating effect is modeled by embedding temperature increment into free-carrier mobility model, and the trapping effect is modeled by introducing an indirect variable effective gate voltage $V_{\mathrm {gseff}}$ . Moreover, the scaling and multiharmonic characteristics of the SP model are studied for the first time. The geometry-dependent thermal resistance $R_{\mathrm {ths}}$ is identified by the electrothermal finite-element method simulations, which is scalable with the gate width W and power dissipations $P_{\mathrm {diss}}$ of the device. Single-tone on-wafer load–pull measurements at operating frequency 8 GHz is carried out for verification purpose. Accurate predictions of the static (dc) $I\!-\!V$ , pulsed-gate-and-drain $I\!-\!V$ , S-parameters up to 40 GHz and large-signal harmonic performance (the fundamental, second- and third-harmonics output power, and power-added efficiency) for the devices with different gate peripheries have been achieved by the proposed model. The results of this paper can pave the way for the full application of the physical-based model in circuits design.