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 （G_m） 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 （G_m′ and G_m"） are simultaneously reduced by 37% and 35%， respectively. Meanwhile， the MCGGR-HEMT demonstrates a flatter f_T curve over a wider gate voltage range. At 10 GHz under single-tone continuous-wave （CW） over 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/P_DC） 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.