Abstract: The knowledge of the small-signal equivalent circuit cryogenic model of high electron mobility transistors (HEMT) is crucial for the design of cooled low-noise amplifiers(LNA) and is very useful to support the analysis of the tran sistor microwave performance. This paper describes a method for designing cryogenic L band amplifiers with very low noise for the 1 ~2 GHz frequency range, the design is based on measured cryogenic direct current and scattering-parameters com bined with a small-signal noise model. At room temperature, the HEMT amplifier achieved a power gain greater than 28dB and a maximum noise figure of 39K. When cooled to 11K, the noise temperature can be reduced to 1. 9 ~ 3. 1K, input and output return loss of better than -10dB, and 1dB compress point output power 9. 2dBm with a total power consumption of 54mW.