The Filter bank multi-carrier (FBMC) with offset-quadrature amplitude modulation (OQAM) gained lot of attention recently. Both orthogonal frequency division multiplexing (OFDM) and FBMC-OQAM suffer from high peak-to-average power ratio (PAPR). The classical PAPR reduction schemes suggested for OFDM signals cannot be directly applied on the FBMC-OQAM, due to the overlapping structure. In this paper we investigate the problem of PAPR reduction in FBMC-OQAM systems and a trellis-based selected mapping (TSLM) scheme with dynamic programming (DP) has been proposed, which probes for optimal phase rotation vectors. With selected mapping (SLM) scheme, multiple patterns of the modulated signal are generated. Theoretical and numerical analyses indicate that TSLM offer better PAPR reduction performance as compared to symbol-by-symbol approach. Simulation results show that performance of FBMC-OQAM system with this method is not only superior to any scheme based on symbol-by-symbol approach, but also outperforms that of the OFDM with classical SLM scheme. It has also been shown that this result holds for different prototype filter impulse responses that are more or less localized in time or frequency.