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In this paper, we propose a new PAPR reduction using the hybrid of a partial transmit sequences (PTS) and cascade adaptive peak power reduction (CAPPR) methods with genetic algorithm (GA). These methods are used in an orthogonal frequency division multiplexing (OFDM) system. The OFDM employs orthogonal sub-carriers for data modulation. These sub-carriers unexpectedly present a large peak to average power ratio (PAPR) in some cases. A proposed reduction method consists of these two methods and realizes both advantages at the same time. The proposed method when number of sub-block increases, PAPR is getting small. However, the calculation cost of its selection must be considerably large. We introduce GA method, the total calculation cost becomes drastically reduced. The parameter for simulation used standard WLAN in IEEE 802.11a system. In simulation results, the proposed method shows the improvement on PAPR and also reveals the high performance on bit error rate (BER) of an OFDM system.