Manipulation of electrons in a solid through transmitting, storing, and switching is the fundamental basis for the microelectronic devices. Recently, the electroresistance effect in the ferroelectric capacitors has provided a novel way to modulate the electron transport by polarization reversal. Here, we demonstrate a giant electroresistive ferroelectric diode integrating a ferroelectric capacitor into two-dimensional electron gas (2DEG) at oxide interface. As a model system, we fabricate an epitaxial Au/Pb(Zr(0.2)Ti(0.8))O3/LaAlO3/SrTiO3 heterostructure, where 2DEG is formed at LaAlO3/SrTiO3 interface. This device functions as a two-terminal, non-volatile memory of 1 diode-1 resistor with a large I+/I- ratio (>10(8) at ± 6 V) and I(on)/I(off) ratio (>10(7)). This is attributed to not only Schottky barrier modulation at metal/ferroelectric interface by polarization reversal but also the field-effect metal-insulator transition of 2DEG. Moreover, using this heterostructure, we can demonstrate a memristive behavior for an artificial synapse memory, where the resistance can be continuously tuned by partial polarization switching, and the electrons are only unidirectionally transmitted. Beyond non-volatile memory and logic devices, our results will provide new opportunities to emerging electronic devices such as multifunctional nanoelectronics and neuromorphic electronics.