The number of matching's in a graph is known as the Hosoya index of the graph. The problem of computing Hosoya index is #P-complete. If the adjacent edges are sequentially ordered, then we show that a polynomial algorithm can be designed. The significance of this algorithm is demonstrated by computing Hosoya index for certain chemical compounds such as Pyroxene. This algorithm can be applied to grid like chemical compounds such as sodium chloride, carbon nanotubes, naphtalenic nanotube etc.