Aiming at the high computational complexity of traditional selective mapping(C-SLM) algorithm, an improved grouping(G-SLM) algorithm is proposed. Without increasing the computational complexity of the system, the number of time-domain candidate signals is increased from M to M 24, and the optimal α value is determined by simulation. In view of the limited peak-to-average power ratio(PAPR) suppression performance of C-SLM algorithm, a μ-GSLM joint algorithm is proposed by combining G-SLM algorithm with μ-law compression expansion method, which further reduces the PAPR of the system. The simulation results show that when complementary cumulative distribution function(CCDF) is 10-3, the PAPR of μ-GSLM algorithm is reduced by 7.5 dB, 3.2 dB and 2.1 dB respectively compared with the original signal, G-SLM algorithm and μ-law compression expansion method.