The bulk and surface magnetoplasmon modes of a Cantor-type superlattice, in which the cells consist of two alternating materials with their thicknesses following the Cantor sequence, are studied in the static approximation. The dispersion relations of the modes are presented concisely in terms of the transfer matrix elements. The authors find that the modes have fractal structure due to the special geometry of the superlattice. As a result of lowering the symmetry by applying an external magnetic field, the propagations of the surface magnetoplasmon become non-reciprocal. By plotting the profiles of the scalar potential amplitudes, they have also investigated the localization properties of the modes.