A generalized carrier index differential chaos shift keying with simultaneous wireless information and power transfer (GCI-DCSK SWIPT) scheme, is proposed, which is an improved scheme for CI-DCSK SWIPT. Compared to CI-DCSK SWIPT, GCI-DCSK SWIPT is not only more flexible in selecting both index bit number and index carrier number, but also is more practical for considering both path loss and the conversion noise generated by radio frequency (RF) band to baseband. The proposed scheme applied a time-switching manner to harvest the energy carried by the inactive carriers. Theoretical bit error rate (BER) expressions of the scheme over AWGN and multipath Rayleigh fading channels are derived, and the ratio of harvested energy to transmitted energy is derived to desecribe the probability of self-sufficiency on power supply. In addition, the frame-derived factor and the energy carried by inactive carriers are optimized to obtain better BER performance. Simulation results show that taking both path loss and conversion noise into consideration, the scheme is still self-sufficient with good BER performance. Furthermore, by adjusting the number of active carriers of GCI-DCSK SWIPT, some cases of GCI-DCSK SWIPT outperform conversion noise-aware CI-DCSK SWIPT in BER.