In order to detect the weak radio signal, the telescope receiver requires good noise performance. As the key circuit of the receiver front end, the noise coefficient and gain of the low noise amplifier (LNA) determine the noise performance of the whole machine. A 1.2--2.2 GHz low noise amplifier is designed. The circuit adopts a two-stage cascade structure. The second stage introduces negative feedback to improve the gain flatness and broaden the bandwidth while reducing the noise. After the post-stage input impedance optimization, only one capacitor is needed between the stages. Lossy output matching network is introduced to realize high gain, low noise, good return loss and flat broadband LNA design. The test results show that the gain is 30--33 dB in the 1.2--2.2 GHz band, the average noise temperature is 47 K, and the output 1 dB compression point is greater than 11.3 dBm. Test results show that the device has good performance, which can be used in the receiver system in this frequency band.