We report a back gate field effect transistors (FETs) with few layers MoS2 nanosheet controlled by PZT ferroelectric gating. The MoS2 transistors with PZT gating (MoS2-PZT FETs) exhibit reproducible hysteresis and nonvolatile memory behaviors with high stability, which can be attributed to the polarization screening from interface adsorbates and charge dynamic trapping/de-trapping into the interface defect states. The ON/OFF states ratios and memory windows have a little change with the channel scaling from 2 μm to 200 nm , revealing the channel scaling hasn’t obvious influence on MoS2-PZT FET properties, which suggests MoS2-PZT FETs promising candidate for future memory applications.