High microwave-noise performance is realized in AlGaN/GaN metal-insulator semiconductor high-electron mobility transistors (MISHEMTs) on high-resistivity silicon substrate using atomic-layer-deposited (ALD) Al2O3 as gate insulator. The ALD Al2O3/AlGaN/GaN MISHEMT with a 0.25- ??m gate length shows excellent microwave small signal and noise performance. A high current-gain cutoff frequency fT of 40 GHz and maximum oscillation frequency fmax of 76 GHz were achieved. At 10 GHz, the device exhibits low minimum-noise figure (NFmin) of 1.0 dB together with high associate gain (Ga) of 10.5 dB and low equivalent noise resistance (Rn) of 29.2 ??. This is believed to be the first report of a 0.25-??m gate-length GaN MISHEMT on silicon with such microwave-noise performance. These results indicate that the AlGaN/GaN MISHEMT with ALD Al2O3 gate insulator on high-resistivity Si substrate is suitable for microwave low-noise applications.