In this study, we propose an optimized AlGaN/GaN high-electron-mobility transistor (HEMT) with a considerably improved breakdown voltage. First, we matched the simulated data obtained from a basic T-gate HEMT with the measured data obtained from the fabricated device to ensure the reliability of the simulation. Thereafter, to improve the breakdown voltage, we suggested applying a gate-head extended structure. The gate-head-top and gate-head-bottom lengths of the basic T-gate HEMT were symmetrically extended by 0.2 μm steps up to 1.0 μm. The breakdown voltage of the 1.0 μm extended structure was 52% higher than that of the basic T-gate HEMT. However, the cutoff frequency (fT) and maximum frequency (fmax) degraded. To minimize the degradation of fT and fmax, we additionally introduced a gate-recessed structure to the 1.0 μm gate-head extended HEMT. The thickness of the 25 nm AlGaN barrier layer was thinned down to 13 nm in 3 nm steps, and the highest fT and fmax were obtained at a 6 nm recessed structure. The fT and fmax of the gate-recessed structure improved by 9% and 28%, respectively, with respect to those of the non-gate-recessed structure, and further improvement of the breakdown voltage by 35% was observed. Consequently, considering the trade-off relationship between the DC and RF characteristics, the 1.0 μm gate-head extended HEMT with the 6 nm gate-recessed structure was found to be the optimized AlGaN/GaN HEMT for high-power operations.