In this thesis, we consider OFDM system and a technique of reduction peak-to-average power ratio (PAPR). The objective is to reduce the PAPR with better performances than those of the clipping method. A good method of reduction PAPR has less in-band and out-of-band radiation of the distortion components and gives a reliable communication. To get our objective, we propose a distortion function for overall signals and mathematically analyze the new method. In addition, we show the proposed method can be applied to the case with frequency offset and propose another approach for OFDM system with lower PAPR.