Graphene and other two-dimensional materials have received considerable attention regarding their potential applications in nano-electronics. Here, we report top-gate nonvolatile memory field-effect transistors (FETs) with different layers of MoSe2 nanosheets channel gated by ferroelectric film. The conventional gate dielectric of FETs was replaced by a ferroelectric thin film that provides a ferroelectric polarization electric field, and therefore defined as an Fe-FET where the poly (vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) was used as the gate dielectric. Among the devices with MoSe2 channels of different thicknesses, the device with a single layer of MoSe2 exhibited a large hysteresis of electronic transport with an over 10(5) write/erase ratio, and displayed excellent retention and endurance performance. The possible mechanism of the device's good properties was qualitatively analyzed using band theory. Additionally, a comprehensive study comparing the memory properties of MoSe2 channels of different thicknesses is presented. Increasing the numbers of MoSe2 layers was found to cause a reduced memory window. However, MoSe2 thickness of 5 nm yielded a write/erase ratio of more than 10(3). The results indicate that, based on a Fe-FET structure, the combination of two-dimensional semiconductors and organic ferroelectric gate dielectrics shows good promise for future applications in nonvolatile ferroelectric memory.