This work presents a novel high-linearity AlGaN/GaN high electron mobility transistor (HEMT) featuring a multi-cycle graded gate recess (MCGGR). The MCGGR-HEMT is realized through a designed periodically graded barrier layer along the gate width direction fabricated using optimized electron beam lithography (EBL) photoresist reflow process. The fabricated MCGGR-HEMT successfully achieves transconductance (Gm) compensation via the parallel connection of multiple periodic devices with graded threshold voltages along the gate width, exhibiting a recordable broadened gate voltage swing (GVS) of 3.5 V. This represents an extension of 1.8 V compared to the 1.7 V of conventional devices. Owing to its continuous graded modulation effect on the 2DEG channel, the higher-order peak transconductance values (Gm' and Gm") are simultaneously reduced by 37% and 35%, respectively. Meanwhile, the MCGGR-HEMT demonstrates a flatter ft curve over a wider gate voltage range. At 10 GHz under single-tone continuous-wave (CW) ower measurement (drain bias of 30 V), it achieves a power density of 5 W/mm and a power-added efficiency (PAE) of 49%. In two-tone CW power measurement at the same frequency (10 MHz tone spacing, drain bias of 30 V), the proposed device delivers a third-order output intercept point (OIP3) of 38 dBm, an OIP3/width of 63.1 W/mm, a linearity figure-of-merit (OIP3/PDC) of 10 dB, and a third-order intermodulation distortion (IMD3) of -57.7 dBc. These performance metrics represent improvements of 5.2 dB, 44 W/mm, 4.8 dB, and 13.7 dB, respectively, over the conventional device. This innovative technology is highly compatible with the conventional GaN HEMT fabrication processes, offering a simplified and cost-effective route for enhancing device linearity.