With the development of the dense wavelength division multiplexer (DWDM) technique, asymmetrical interleaver is emerged. It can be used in optical add-drop multiplexer (OADM) system and other complex networks. Michelson-Gires-Tournois interferometer (MGTI) interleaver is one of the typical schemes. It has the characteristics of compact size, low cost, simple parameters, high performance and so on. The theoretical iteration to determine the period of the MGTI interleaver is deduced from mathematical aspect, and some examples are given in detail to support it. When the reflectances of Gires-Tournois etalon (GTE) mirrors are changed, the characteristics of the intersection of the odd and even output spectrum for symmetrical and asymmetrical interleavers are different. Examples of these different characteristics are given. These conclusions will be useful for designing interleavers based on MGTI that have specified period and bandwidth characteristics. It also has instructional function for the design of special optical interference filter.