Orthogonal frequency division multiplexing (OFDM) and single-carrier frequency domain equalization (SC-FDE) are two commonly adopted modulation schemes for frequency-selective channels. Compared to SC-FDE, OFDM generally achieves higher data rate, but at the cost of higher transmit signal peak-to-average power ratio (PAPR) that leads to lower power amplifier efficiency. This paper proposes a new modulation scheme, called flexible multi-group single-carrier (FMG-SC), which encapsulates both OFDM and SC-FDE as special cases, thus achieving more flexible rate-PAPR trade-offs between them. Specifically, a set of frequency subcarriers are flexibly divided into orthogonal groups based on their channel gains, and SC-FDE is applied over each of the groups to send different data streams in parallel. We aim to maximize the achievable sum-rate of all groups by optimizing the subcarrier-group mapping. We propose two low-complexity subcarrier grouping methods and show via simulation that they perform very close to the optimal grouping by exhaustive search. Simulation results also show the effectiveness of the proposed FMG-SC modulation scheme with optimized subcarrier grouping in improving the rate-PAPR trade-off over conventional OFDM and SC-FDE.