Multicarrier faster-than-Nyquist (MFTN) signaling is a high spectral efficiency transmission scheme, which is promising in the future communication. One of the major problems of MFTN signaling is high peak-to-average power ratio (PAPR). Therefore, PAPR reduction is necessary in MFTN systems. Generally, four times oversampling is used in PAPR reduction methods for MFTN signaling to make the discrete time MFTN signaling approximate the peak of continuous time MFTN signaling. However, generating four times oversampled discrete time MFTN signaling will increase the computational complexity of PAPR reduction methods. In this paper, we propose three new low-complexity PAPR reduction methods based on selective mapping (SLM) for MFTN signaling. The first step of proposed methods is using discrete time MFTN signaling with oversampling factor lower than four as reference discrete signal. Then, three new methods utilize picking, reconstructing, and filtering, respectively, to acquire the peak power of four times oversampled MFTN signaling. It is shown that the proposed methods can significantly reduce the computational complexity while almost without PAPR reduction performance loss. INDEX TERMS Multicarrier faster-than-Nyquist (MFTN), peak-to-average power ratio (PAPR), selective mapping (SLM), low-complexity. BIAO CAI received the B.S. degree in communication engineering and the M.S. degree in communications and information system from the College of Communications Engineering, PLA