Abstract: Taylor series expansion theorem is a very important method for the construction of finite difference.For ex- ample,2-order Taylor central finite difference is adopted in Yee format and 4-order in Fang format.With the knowledge of linear algebra,general formula for arbitrary order Taylor finite difference(TFD)has been derived.In this paper,the analy- sis of spectral property and computational error of arbitrary order TFD is presented in detail.Then it is applied into the nu- merical solution of Maxwell's equations.Stability condition and numerical dispersion relation are derived.And what's more,a new definition of error is introduced for evaluation of the computation.The effect of Courant number,grid resolution (CPW)and ratio of cell on numerical dispersion is analyzed too.