A Sagnac-type Mach-Zehnder interferometer(SMZI) is a very stable instrument with respect to phase drift because all optical paths can share common optical components. We have observed very stable interference fringes in single photon interference experiments with an extremely attenuated laser beam, and with heralded single photons prepared from polarization correlated photon pairs in type-II spontaneous parametric down-conversion. The phase stability is measured to be about ${pm}0.18$ rad for the SMZI, in contrast, conventional MZI showed the phase fluctuation of around ${pm}1.02$ rad.