The periodic reflections in frequency were observed in a stack of graphene layers and reported as a series of mini photonic bandgaps owing to the multiple interference by the graphene layers. In this research, the effective medium approach was employed to obtain the effective refractive index and Bloch impedance for understanding the wave propagation characteristic therein. Specifically, the pure real effective refractive index without attenuation as well as an extremely low Bloch impedance were found at the frequencies exhibiting periodic reflections. Some numerical examples were demonstrated to show that the series bandgap-like reflections in fact are attributed to considerable impedance mismatch caused by this ultra low Bloch impedance.