High peak-to-average power ratio (PAPR), a main problem of 5G Filtered-Orthogonal Frequency Division Multiplexing (FOFDM) system, seriously affects the system’s transmission effciency. Aiming at the shortcomings of the traditional selectivemapping (SLM) algorithm, the grid scroll chaotic extended sequence (GSCES) algorithm is proposed to solve the high PAPRproblem. The proposed grid multiscroll chaotic maps are used as random phase sequence vectors instead of the traditional pseudorandom sequence, which provide a large number of random sequences with good correlation characteristics, random characteristics, and high security. The proposed random phase sequence vectors can meet the needs of 5G mass connections. Theoriginal input signals are divided into real part and imaginary part, which are, respectively, dot produced with the proposed gridmultiscroll chaotic maps. €e numerical simulation results show that the proposed GSCES algorithm effectively increases thenumber of candidate sequences, reduces the PAPR values, and improves the transmission effciency and security. Moreover, thehardware experimental results produce at 2×2×2-grid multiscroll chaotic attractor, which further proves the physical realizationof the proposed system. The proposed schemes have a broad application prospect in 5G multicarrier modulation technology.