Recently, filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) has received increasing attention from researchers, owing to its merits and superior spectral efficiency. High peak-to-average power ratio (PAPR) occurs in approximately all multicarrier systems, including FBMC/OQAM, and may cause bit-error-rate (BER) degradation if not appropriately handled. Conventional PAPR reduction methods for orthogonal frequency division multiplexing (OFDM), such as partial transmit sequence (PTS), selective mapping (SLM), and discrete Fourier transform (DFT) spreading, are ineffective in FBMC/OQAM because of the different structure of the symbols. This study proposes a novel method combining DFT spreading and PTS methods to reduce the PAPR of FBMC/OQAM systems with reasonable computational complexity. Numerical results obtained from various computer simulations show that the proposed method achieves a noticeable enhancement in the PAPR performance of the FBMC/OQAM signal compared to other existing methods without affecting the BER performance. Further, the computational complexity analysis and BER performance of the proposed method are presented in comparison to typical existing methods. From our computer simulations, the proposed method reduces the PAPR by approximately 32.8% compared to that of the conventional methods, and the BER performance is improved by 25% with a high-power amplifier effect.