Abstract: The reservoir simulation based on PEBI grid can simulate more accurately.Its major calculation is to solve the finite difference equation which is based on the PEBI grid.In order to speed up the process and minimize the data storage，a method to optimize the numbering of PEBI grid through the spectral algorithm is presented，which can minimize the bandwidth of matrix which represents the finite difference equation’s coefficient.There are three main steps in this algorithm.First，calculate the adjacent matrix of the grid and its Laplacian matrix in accordance with the original numbering.Then，get the Fiedler vector by computing the eigenvalues and eigenvectors of the Laplacian matrix.At last，sort the Fiedler vector through the quick sort，and renumber the grids according to the sorted Fiedler vector.In the end，the good result of PEBI grid’s numbering optimization through spectral algorithm is proved by experiment.