Self-rectifying memristor has no need for selector devices, but possess the one-way transmission behavior and multi-level non-volatile memory characteristics, which makes it promising candidate for electronic synapse. In this letter, we propose a novel self-rectifying memristor based on Pt/Hf0.5Zr0.5O2/TiN structure. The devices show large memory window (104) and high rectifying ratio (104), which can block the sneak current in passive crossbar array without any additional hardware overhead. Moreover, the devices demonstrate excellent multi-level states modulation capability, low power consumption, high endurance and long retention. The final benchmark demonstrates that the proposed Pt/Hf0.5Zr0.5O2/TiN self-rectifying memristor is a promising candidate for electronic synapse application.