Abstract: In view of the problem of high peak-to-average power ratio (PAPR) in the existing multi-carrier modulation method of prolate spheroidal wave functions (PSWFs) signal based on signal grouping optimization, a multi-carrier index modulation method of PSWFs signal based on continuous phase modulation (CPM) is proposed. The CPM modulation with coding characteristics is used as the constellation symbol mapping method, and PSWFs signal is used as index carrier waveform to generate the modulated signal. The maximum likelihood (ML) detection and CPM differential decoding are used to realize the detection and demodulation of the receiving signal. The method can effectively reduce the PAPR about 2.90dB of the existing method modulation signal, with a small bit error ratio (BER) performance loss and appropriate increase in algorithm implementation complexity.