To solve the crosstalk problem when the integration density of resistive random access memory (RRAM) devices increase, RRAM with self-rectifying function is required. Herein, the Au/10 nm Al2O3/heavily doped p-type Si (p++-Si) structure was fabricated, and bipolar resistive switching and self-rectifying effect were investigated. A rectification of 6.5 × 103 under ±5 V at low-resistive state (LRS) was observed. The rectifying effect is explained by the energy band diagrams of the structure and electrical conduction mechanism at LRS under negative bias is fitted by space charge limited conduction (SCLC) model. Finally, the endurance and retention properties of the structure were tested. This work would provide insights for further research on the RRAM device with self-rectifying effect, which can alleviate the crosstalk effect without additional switching elements in integrated circuit.