Low Noise Amplifier (LNA) is generally the first stage in microwave communication system. The quality factor of the receiver is greatly determined by the performance of LNA. Design of a low noise amplifier (LNA) is a very critical as it amplifies the received signal and contributes most of the noise figure of whole receiver. LNA is an integral component of RF receiver and it performs various functions i.e. amplification, noise reduction, Noise Figure reduction, better stabilization and noise immunization. However, design of a LNA requires the tradeoff of many important parameters including gain, Noise Figure (NF), stability, power consumption, cost and design complexity. In this paper, we have designed and optimize the performance of a single stage stable LNA through an optimization algorithm. Our optimized single stage LNA circuit provides a gain of 11.78 dB and noise figure of 1.86 dB. These are the most important design parameter of a LNA. In this design, a microwave BJT numbered AT3103 from Avago technologies was used. The simulation and performance optimization was carried out in Agilent design package Advance Design Systems (ADS). This LNA operates at center frequency of 2 GHZ and it can be used in L-Band satellite applications.