A 23-31 GHz three-stage low noise amplifier (LNA) based on a 100 nm Gallium Nitride (GaN) on Si technology is presented with a total circuit size of 2.0×1.4 mm2. To perform excellent noise figure (NF) and gain, a special inductive dual-source feedback network is utilized, which is contribute to noise matching and input conjugate matching by resonating with the equivalent gate-source capacitance of the transistor. The T-type network and reactive/resistive network are carefully employed for broadband matching circuits to extend the bandwidth. Meanwhile, a lossy RLC feedback network of the output stage can further obtain a wider frequency band and improve the stability though miller approximation analysis of the input quality factor and gain of closed-loop system. In this letter, the LNA achieves a noise figure of 1.9-2.5 dB, a small signal gain of 24-27 dB and the 1-dB compression point output power (OP1dB) of 16 dBm across the band.