Abstract: One problem of the reconstruction conjecture is：find a complete set of invariants of a graph. The spectral moment sequence is an important invariant of a graph，since the kth spectral moment of a graph is equal to the number of closed walks of length k. On the structure feature of a graph，first finds all connected subgraphs which can generate closed walks of length eight ，then provides 8th spectral moment calculation formula.

Key words: Adjacent matrix , kth spectral moment , star , unicyclic graph , bicyclic graph