Weighted overlap and add-orthogonal frequency division multiplexing (WOLA-OFDM) is a new waveform proposed recently for meeting the requirements of fifth generation (5G) telecommunication standards. In spite of being a serious 5G waveform candidate, WOLA-OFDM is exposed to the problem of high peak to average power ratio (PAPR) similar to the other waveforms in which multicarrier transmission strategy is employed. Due to the overlapping nature of WOLA-OFDM waveform, where the extension of the current symbol is overlapped with the extension of the previous symbol, it will not be efficient to apply conventional PTS (C-PTS) directly to the WOLA-OFDM waveform. Therefore, in this paper, we propose dual symbol optimization-based partial transmit sequence (DSO-PTS) technique for PAPR reduction in WOLA-OFDM waveform. In our proposed technique, two adjacent symbols are jointly considered when searching for the optimal data block with minimum PAPR unlike the C-PTS where the adjacent symbols are optimized individually. In the simulations, our proposed DSO-PTS technique, C-PTS, and GreenOFDM that is developed recently by modifying the conventional selective mapping (SLM) method are compared with each other with regard to PAPR reduction performance for different search numbers (SNs). In addition, the effects of DSO-PTS, C-PTS, and GreenOFDM on the amount of out of band (OOB) radiation in the power spectral density (PSD) graph of WOLA-OFDM employing solid state power amplifier (SSPA) is measured for different SNs and input back off (IBO) values. According to the simulation results, our proposed DSO-PTS technique clearly demonstrates a superior PAPR reduction and PSD performance.