Based on a detailed analysis of the Slepian function, the advantages and disadvantages of the application of the Slepian function in computing lunar local gravity model, local power spectrum combined with the CEGM02 model and local admittance and correlation based on CEGM02, SGM150j, LP150Q and GRAIL660 were analyzed in this paper. It turns out that the local orthogonal Slepian function shows obvious advantages in modeling lunar local gravity field. In the application of power spectrum, the method of Slepian model shows a much wider, credible and reliable bandwidth but brings greater uncertainty in high degrees with the abnormal signal on the cap edge. On the contrary, the local power spectrum curve of Slepian window reflects the relationship between local gravity and the whole moon, but the spectral curve shows a narrow reliable bandwidth and significant errors in low degrees. Local admittance and correlation of four gravity models shows small difference in low orders but obvious difference as the orders get higher.
