We experimentally demonstrated a new concept of non-destructive read-out process using transconductance measurements for ferroelectric random-access memory (FeRAM) using a graphene layer as the channel material of bottom-gated field effect transistor. With a 200 nm thick PZT (Lead Zirconate Titanate) layer as the ferroelectric film, the transconductance of graphene channel is found to change depending on the direction of spontaneous polarization (SP) of the ferroelectric layer. The transconductance for upward SP is estimated to be ~25 μS and that for downward SP be ~4 μS when the operational characteristics of Graphene/Al2O3/PZT/Pt/Ti field effect transistor fabricated on a SiO2/Si substrate are measured. Here, the Al2O3 and Pt/Ti layer act as gate insulator and gate electrode, respectively. From the 24-hour retention test, it is also confirmed that the transconductance stays well-distinguishable for the two opposite directions of SP in the ferroelectric layer. This indicates that the memory state specified by the SP direction can be read out reliably from transconductance measurements. With the proposed read-out method, it is possible to construct an array of ferroelectric memory cells in the form of cross-point structure where the transconductance of a crossing cell can be measured selectively without any additional selector. This type of FeRAM can be a plausible solution for fabricating high speed, ultra low power, long lifetime, and high density 3D stackable non-volatile memory.