Memristors are designed to mimic the brain's integrated functions of storage and computing, thus breaking through the von Neumann framework. However, the formation and breaking of the conductive filament inside a conventional memristor is unstable, which makes it difficult to realistically mimic the function of a biological synapse. This problem has become a main factor that hinders memristor applications. The ferroelectric memristor overcomes the shortcomings of the traditional memristor because its resistance variation depends on the polarization direction of the ferroelectric thin film. In this work, an Au/Hf 0.5 Zr 0.5 O 2 /p +-Si ferroelectric memristor is proposed, which is capable of achieving resistive switching characteristics. In particular, the proposed device realizes the stable characteristics of multilevel storage, which possesses the potential to be applied to multi-level storage. Through polarization, the resistance of the proposed memristor can be gradually modulated by flipping the ferroelectric domains. Additionally, a plurality of resistance states can be obtained in bidirectional continuous reversibility, which is similar to the changes in synaptic weights. Furthermore, the proposed memristor is able to successfully mimic biological synaptic functions such as longterm depression, long-term potentiation, paired-pulse facilitation, and spike-timing-dependent plasticity. Consequently, it constitutes a promising candidate for a breakthrough in the von Neumann framework.