Abstract Based on a model a little bit complicated than that in ref.  , the mathematical method of ref.  was used to yield an universal condition of dispersion. By means of this condition, the surface plasmon spectra of the quasiperiodic semiconductor superlattice of type-I, type-II and II-VI compounds were discussed.The results show that bacause of the break of reflection symmetry in the plane perpendicular to the axis of the superlattice, when the surface is located at the Fm different interfaces of the primary cell, the spectrum of surface plasmon shows a great deal of patterns for each choice of sets of the parameters. (Fm is the Fibonacci number).