To improve the performance of belief propagation multi-target tracking under dense clutter interference, an amplitude clutter suppression-based Gaussian mixture belief propagation (GMBP-AC) multi-target tracking method was proposed. First, based on the classical Rayleigh distribution model, the initial signal-to-noise ratio (SNR) of target was estimated by the maximum likelihood estimation. The truncated normal distribution model for the SNR of target was constructed with the combination of prior information and then marginalized. Next, based on the amplitude information, the amplitude likelihood ratio (ALR) of each measurement was calculated before belief propagation and introduced into the measurement information function, which improved the association accuracy between targets and measurements. Finally, the measurement information admission rate was set to get the lower limit of ALR, and the measurements of all the sensors were selected to complete the target initiation efficiently. The research shows that under different SNR and clutter densities, compared with GMPHD, GMBP, and GMBP-AK, the proposed GMBP-AC has higher computational efficiency. The method can respond to the changes of target numbers more accurately and quickly in various time periods, and meanwhile reduce the OSPA error greatly. It further proves that under dense clutter interference, the proposed method has high efficiency of clutter suppression, and can improve the target numbers estimation performance and multi-target tracking accuracy.