LoRa is a widely recognized modulation technology in the field of low power wide area networks (LPWANs). However, the data rate of LoRa is too low to satisfy the requirements of Internet of Things applications. To address this issue, we propose a novel high-data-rate LoRa scheme based on the spreading factor index (SFI). In the proposed SFI-LoRa scheme, the starting frequency bin of a chirp signal is used to transmit information bits, while the combinations of spreading factors are exploited as a set of indices to convey additional information bits. Moreover, the theoretical symbol error rate, data rate, transmission throughput, complexity and energy efficiency of the proposed SFI-LoRa scheme are carefully analyzed. Simulation results not only verify the accuracy of our theoretical analysis, but also demonstrate that the proposed SFI-LoRa scheme can improve the transmission throughput of existing LoRa schemes without sacrificing the BER performance over additive white Gaussian noise, Rayleigh fading, and multipath flat-fading channels. Therefore, the proposed SFI-LoRa scheme is a potential solution for applications requiring a high data rate in the LPWAN domain.