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 in the context of modern Internet of Things (IoT) 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 (SFB) of chirp signals is used to transmit information bits, while the combinations of spreading factors (SFs) are exploited as a set of indices to convey additional information bits. Moreover, theoretical expressions for the symbol error rate (SER) and throughput of the proposed SFI-LoRa scheme are derived over additive white Gaussian noise (AWGN) and Rayleigh fading channels. Simulation results not only verify the accuracy of the theoretical analysis, but also demonstrate that the proposed SFI-LoRa scheme improves both the bit error rate (BER) and throughput performance compared to existing high-data-rate LoRa schemes. Therefore, the proposed SFI-LoRa scheme is a potential solution for applications requiring a high data rate in the LPWAN domain.