Design optimization of microwave circuits is a crucial matter for microwave engineers. For the last decades, researchers had been studying surrogate models for a computationally efficient design optimization process. Artificial Intelligence based algorithms had been used for modelling of complex microwave stages such as antenna, amplifiers and frequency selective surfaces. In this study, design optimization of a Low Noise Amplifier (LNA) based on surrogate models for both transistor stage and input & output matching circuits had been presented. Support Vector Regression Machine had been used for creating surrogate models of a microwave transistor and a non-uniform transmission line for having a fast and accurate LNA design optimization process alongside a low profile and high performance LNA using on-uniform transmission lines. By using this methodology, not only designer can create a mapping for missing points in the sparse sample S parameter data points provided by manufacturers but also the overall simulation duration can be significantly reduced thanks to the fast nature of surrogates compared to EM simulators. Here, the proposed surrogate models had been used alongside of Particle Swarm Optimization algorithm to determine optimal geometrical values of input/output matching networks. Then the obtained designs are prototyped and measured. The measured results are also compared with the performance results of counterpart design in literature. As for results, not only the proposed methodology is an effective, fast and reliable method for computationally efficient design optimization process of LNA but also provides better results than the counterpart design in literature.