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In this work, we demonstrated high-performance, non-volatile MoS₂ field effect transistors (FETs) with polycrystalline ferroelectric PbZr_0.35Ti_0.65O₃ back gate. We mechanically exfoliated few-layer MoS₂ flake and transferred it onto 300 nm polycrystalline PZT films, which possesses high dielectric constant of 650, and then fabricated samples into 2-point devices. We characterized the transfer characteristics of the MoS2 FET at gate voltage below the coercive voltage of PZT. The PZT behaves as a high-k dielectric, which can induce high current ratio of 10⁷ in MoS2 within a gate voltage range of ±0.5 V. The devices also showed ultra-low sub-threshold swing (SS) of about 52 mV/dec at room temperature, transcending the 60 mV theoretical limit for classical FET, which may originate from the negative capacitance effect of the ferroelectric gate.