Coronoid systems are natural graph representations of coronoid hydrocarbons associated with benzenoid systems, but they differ in that they contain a hole. The Hosoya index of a graph G is defined as the total number of independent edge sets, that are called k-matchings in G. The Hosoya index is a significant molecular descriptor that has an important position in QSAR and QSPR studies. Therefore, the computation of the Hosoya index of various molecular graphs is needed for making progress on investigations. In this paper, a method based on the transfer matrix technique and the Hosoya vector for computing the Hosoya index of arbitrary primitive coronoid systems is presented. Moreover, the presented method is customized for hollow hexagons by using six parameters. As a result, the Hosoya indices of both each arbitrary primitive coronoid system and also each hollow hexagon can be computed by means of a summation of four selected multiplications consisting of presented transfer matrices and two vectors.