GaN high-electron-mobility transistors (HEMTs) have no avalanche capability and are known to fail electrically when the transient overvoltage reaches their dynamic breakdown voltage (BVdyn). This work explores the failure mechanism of GaN HEMTs in continuous overvoltage switching at high frequency. Three commercial GaN HEMTs with different device structures and voltage ratings are studied . Two DUTs show the electrical failure at BVdyn consistently under different switching frequencies. A new failure behavior is observed in the third DUT, where the electrical failure dominates at low frequencies and the thermal failure occurs at high frequencies with an overvoltage boundary lower than BVdyn. This failure mechanism is found to be tightly correlated with the drastic, nearly-unrecoverable on-resistance (RON) increase during the overvoltage switching at high frequency. These results reveal a new overvoltage failure mode of GaN HEMTs and suggests a new overvoltage boundary lower than BVdyn in high-frequency overvoltage switching.