The goal of proposed research is to construct the circular polarized narrow-band directed antenna using low-loss dielectric and high relative permittivity material for the substrate. Presented first part contains the simulation of such antenna using the software which based on Finite Element Method for the purpose to fined optimal parameters of such antenna before its construction. Using numerical experiment we suppose to determine best parameters of antenna, to achieve desired radiation parameters: well matched to the open space; circular polarization of radiated field; narrow-beam; wide-ban. It was designed 2.49 GHz and 2.4 GHz circular polarization radiation patch antennas, which was archived by cutting edges from square patch antenna. For simulation it was used 6.8 relative permittivity material for the substrate.