This paper investigates a novel design for joint radar-communication (JRC) waveform, which is capable of improving the network’s performance by solving the phase shift mutation of the Chirp-BPSK waveform. We aim for jointly designing chirp waveform and improving Binary Phase Shift Keying (BPSK), as well as the hybrid chaotic spread spectrum code (CSSC). As a benefit, the JRC waveform can be successfully decoded, and the accumulation of phase shift can be suppressed by hybrid CSSC. The detailed deduction on the short-time Fourier transform (STFT) of the JRC waveform is adopted to analyse the complicated AF characters. Our analytical results demonstrate that the proposed JRC signal has superior spectrum performance, ambiguity function (AF), and transmission rate than conventional Chirp and Chirp-BPSK waveform. Numerical results are provided to confirm that (i) the proposed waveform is capable of providing better communication and radar performance; (ii) the performance of AF is not affected by the transmission rate for the proposed waveform.