LoRa is a proprietary technology for IoT (Internet of Things) applications and it has attracted widespread interest from both academia and industry in recent years. As the core technique of LoRa physical (PHY) layer, chirp spread spectrum (CSS) modulation is adopted to support long range communications. In this letter, we propose a novel group-based CSS (GCSS) modulation scheme and introduce a new configurable parameter called group number (GN) as an enhancement to LoRa PHY layer with the aim of achieving a more extensive and flexible trade-off between power and spectral efficiency. Moreover, by exploiting the intrinsic properties of GCSS modulation, we prove that the maximum spectral efficiency can reach up to 0.5 bps/Hz. Simulation results of BER (bit error rate) performance in both AWGN and Rayleigh fading channels are presented to verify the feasibility and advantage of this new modulation scheme.