A novel Eigenvector Method(EM) for the calculation of resonator modes and beam propagation is developed.A new transit matrix for the optical resonator is obtained based on the Fresnel-Kirchhoff diffracted integral equation.The eigenvectors of the transit matrix,that represent multi-mode characteristics of the resonator,are calculated with the integral eigen-equation.The field inside or outside the resonator resulting from the eigenvectors can be derived by EM as well.The partition of grids,choice of shape functions,error and convergence analyses are discussed.It shows that a suitable partition of grids and choice of shape functions are of benefit to increase calculation rate,precision and stability.