In this paper, we investigate the problem of a wide-gap frequency hopping sequence (WGFHS) in a cognitive frequency hopping (CFH) system. The CFH system can achieve more reliable communication in a complex electromagnetic environment than does a conventional frequency hopping (FH) system. Moreover, an appropriate WGFHS could minimize the impact of jamming on the CFH system. However, conventional WGFHS adopted in the CFH system performs poorly in statistical properties and FH synchronization. Therefore, we propose an algorithm called the classified pseudorandom perturbation (CPRP) that can generate a random and uniform WGFHS with its uniform distribution keeping invariable during wide-gap mapping. In addition, it can achieve a high FH synchronization probability because all of the required parameters can be obtained from the known real-time status and sensing results. The simulation results indicate that the WGFHS generated by the CPRP outperforms the existing WGFHSs, such as the Reed-Solomon (RS) code with dual subbands (DSBs) and the chaotic sequences with shifting replacement.