Design method on broad-band low noise multistage amplifier is considered. This method consists of two parts. First, by the analytical matching theory approximate circuit element values are obtained. Second, by computer optimization, we can obtain the optimized network element values which satisfy the given specifications more sufficiently. And by this design method, using GaAs MESFET 4 stage high gain, low noise amplifier is designed. Also, consideration point on multistage amplifier is stated.