In this paper, a new waveform called discrete Fourier transform spread orthogonal frequency division multiplexing with chirp modulation (DFT-s-OFDM-CM) is proposed for the next generation of wireless communications. The information bits are conveyed by not only Q-ary constellation symbols but also the starting frequency of chirp signal. It could maintain the benefits provided by the chirped discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM), e.g., low peak-to-average power ratio (PAPR), full frequency diversity exploitation, etc. Simulation results confirm that the proposed DFT-s-OFDM-CM could achieve higher spectral efficiency while keeping the similar bit error rate (BER) to that of chirped DFT-s-OFDM. In addition, when maintaining the same spectral efficiency, the proposed DFT-s-OFDM-CM with the splitting of information bits into two streams enables the use of lower-order constellation modulation and offers greater resilience to noise, resulting in a lower BER than the chirped DFT-s-OFDM.