In this paper,we have analysed in detail the quantum interference of the degenerate narrowband two-photon state by using a Mach-Zehnder interferometer,in which an electromagneticalty induced transparency (EIT) medium is placed in one of two interfering beams.Our results clearly show that it is possible to coherently keep the quantum state at a single photon level in the EIT process,especially when the transparent window of the EIT medium is much larger than the bandwidth of the single photon.This shows that the EIT medium is possibly a kind of memory or repcater for the narrowband photons in the areas of quantum communication and quantum computer.This kind of experiment is feasible within the current technology.