Orthogonal frequency division multiplexing with Offset Quadrature Amplitude Modulation (OFDM-OQAM) technique has drawn significant interests in recent years. However, most of the existing OFDM peak-to-average ratio (PAPR) reduction schemes cannot be used in the OFDM-OQAM system directly. In this paper, a modified scheme called overlapped segmental Active Constellation Extension (OS-ACE) is proposed to deal with the high PAPR problem specifically in the OFDM-OQAM system. For the proposed OS-ACE scheme, the input signals are divided into a number of overlapped segments and then the ACE operation is processed on each segment. Simulation results show that the modified scheme used in the OFDM-OQAM system can provide better performance than conventional ACE scheme directly used in the OFDM-OQAM system, and even outperforms conventional ACE scheme applied in the OFDM system.