Although the frequency-modulated continuous-wave (FMCW)-based scheme has been considered a candidate for realizing integrated radar-communication (RadCom) systems, it is limited by low spectral efficiency. Thus, this study proposes a frequency hopping-aided FMCW-based RadCom system along with the corresponding radar detection and communication signal demodulation approaches. The proposed system can significantly improve the transmission rate with slight radar performance degradation. In addition, both the radar and communication subsystems of the proposed RadCom system are analyzed. Consequently, a symbol interleaving approach that can mitigate radar performance degradation is proposed. Furthermore, the interference is shown to not degrade the radar performance significantly because of frequency hopping. However, to address the issue of the interference significantly degrading communication performance, interference avoidance and mitigation approaches using scheduling and interference rejection combining, respectively, are proposed. Simulations are conducted to evaluate the proposed RadCom system. The results validate the analysis and demonstrate that the proposed RadCom system can provide radar detection performance that is almost identical to conventional FMCW radar with a high transmission rate. Furthermore, the results confirm the effectiveness of the proposed interleaving and interference management methods.