Memory effect of graphene has been studied in various ways based on the Fermi-level shift driven by external electric field. From the current hysteresis loop obtained by changing the gate voltage of Graphene/SiO2/Si field effect transistor, the existence of two different channel conductivity states has been observed which can be used for a two-level memory device. [1] This phenomenon has been explained by the motion of hydroxides and hydrons ionized from the water molecules trapped between the graphene channel and the SiO2 gate insulator. [2] In this study, we fabricated a CVD-grown graphene field effect transistor on SiO2/Si substrate and found four different channel conductivity states tunable by varying the applied gate voltage pulse. It is shown that the stabilization of the reset state (off-state), which is one of the challenging issues in fabricating memory devices with this phenomenon, can be achieved by positioning the Fermi-level in the off-state as close to the charge neutrality point as possible during read-out. A constant gate voltage which is chosen to ensure the proper positioning of the off-state Fermi-level is always applied in read-out steps. This study demonstrates the possibility of fabricating graphene-based multi-bit memory devices.