According to large-calculation and lower-efficiency of the auxiliary particle filter, an auxiliary marginal particle filter algorithm is proposed based on fast Gaussian transform (FGT-AMPF). Assuming that the state noise is additive and Gaussian, the solution of Chapman-Kolmogorov equation (CKE) for nonlinear filtering, is similar to executing kernel density estimation (KDE). Then FGT of KDE is introduced to improve the calculation efficiency. The simulation results show that the calculation error obtained by the conventional particle can also be gotten by using a small number of particles, and the algorithm greatly improves the calculation efficiency.