Abstract: The coaxial impedance convertor plays a very important role in the field of high power microwave. The impedance of a coaxial line can be converted by gradually changing the diameter of the inner conductor of the coaxial line, and some functions such as the polynomial, the cosine, the exponent and etc，can be applied to describe the curve of the diameter variation. In this paper, the finite-difference time-domain method (FDTD) was used to calculate the reflection coefficient in the coaxial line, and Genetic Algorithm (GA) was adopted to optimize the curve in order to design a convertor with a shortest length of the diameter-changing inner conductor and a minimal reflection coefficient. The optimization calculation of the GA was parallelized in the master-slave model and run in a Beowulf sys