The transfer matrices, which transfer the amplitudes of the electric fields of second- and third-harmonic waves from one side of the interface to the other, are defined for layers joined coherently, and the total transfer matrices for several sequential interfaces can be simply obtained by multiplication of the matrices. Using the transfer matrix method, the interacting processes of second- and third-harmonic waves in a one-dimensional finite Fibonacci dielectric superlattice are investigated. Applying the numerical procedure described in this letter, the dependence of the second- and third-harmonic fields on sample thickness is obtained. The numerical results agree with the quasi-phase-matching theory.