SummaryNon‐orthogonal multiple access (NOMA) is a great contender for future cellular modulation due to its desirable properties like massive connectivity, high data rate transmission, and high spectral efficiency. However, its peak‐to‐average power ratio (PAPR) is significant, which becomes a significant disadvantage for the efficient operability of the NOMA waveform compared to current techniques. Several PAPR reduction algorithms like selective mapping (SLM), partial transmission sequence (PTS), and companding techniques have been proposed to lower the PAPR of multicarrier waveforms (MCWs). PTS reduces the PAPR but has high complexity. On the other hand, SLM has a less complex framework, but its PAPR performance is not as efficient as PTS. Companding methods reduce the PAPR by compressing the signals at the transmitter, which unfortunately reduces the dynamic range of the signal. In this work, we propose a hybrid algorithm (SLM + PTS) with a companding method for the first time for the NOMA waveform, which efficiently reduces the PAPR with low computational complexity. Furthermore, we compare the performances of a host of candidate algorithms like SLM, PTS, hybrid (SLM + PTS), hybrid + A law (SLM–PTS–A law), and hybrid + Mu law (SLM–PTS–Mu law). The results of the experiments show that the hybrid + Mu law did a better job than the existing PAPR reduction algorithms.