In light of increasing requirement for electromagnetic spectrum, spectrum efficiency improvement of radar and communication integration waveform is gaining interest. In this paper, to improve conventional linear frequency modulation (LFM)–continuous phase modulation (CPM) spectrum efficiency, a modified radar and communication integration waveform is proposed. Considering high spectral efficiency of shaped-offset quadrature phase-shift keying (SOQPSK), we generate a new modulation: shaped octal phase-shift keying (S8PSK) by combining the precoding method and CPM with octal phase-shift keying (8PSK). S8PSK is then used to encode communication data into LFM radar signal to form a novel radar and communication integration waveform: LFM-S8PSK. Numerical results demonstrate that compared with LFM–CPM, LFM-S8PSK can provide better spectrum efficiency in exchange for slightly worse bit error rate (BER). Also, it is shown that LFM-S8PSK almost maintains comparable radar performance with respect to LFM.