The point pattern matching algorithm based on the spectral method performs poorly when the two point patterns to be matched are not isomorphic. To improve the matching performance of the spectral method for non-isomorphic point patterns，it is combined with Delaunay triangularization process and a new inexact point pattern matching algorithm is proposed. The algorithm defines the point patterns’ local structures based on Delaunay triangularization to reduce the influenced area of the points that are in one point pattern and have no correspondent in the other. The local structures from the two point pattern are matched with each other using the spectral method. After the most similar local structure pair is found it is used to guide the matching of the remaining points within the two point patterns. Simulation experiments show that the proposed algorithm is superior to the existing point pattern matching algorithms which are based on the spectral method.