The common-source low noise amplifier(LNA) with inductive degeneration using a genetic algorithm is designed and tested for a down converter in an industrial, scientific and medical (ISM) band application and a wireless broadband internet service (WiBro). The genetic algorithm optimizes the reflection coefficients to be well matched the input and output ports between multistage transistor amplifiers, and it generates low voltage standing wave ratio as well as gain flatness of the amplifier. The stability and the gain flatness of the LNA have been improved by combining the matching circuits and the series feedback microstrip lines with inductive degeneration at common-source port. In the frequency range of ISM band and WiBro application operating at $2.3GHz{sim}2.5GHz$, the measured power gain and maximum voltage standing wave ratio (VSWR) of the LNA are $41{pm}0.5dB$ and 1.3, and the noise figure of the LNA is lower than 0.85dB. The above results are agreed well with the theoretical values of the amplifiers.