A distinct unipolar but single-polarity resistive switching behavior is observed in a TiO(x)/Pt/TiO(x) trilayer structure, formed by thermal oxidation of a Ti/Pt/Ti stack. As a comparison, a memory device with a single TiO(x) active layer (without addition of Pt midlayer) is also fabricated but it cannot perform resistive switching. Energy band diagrams are illustrated to realize the modulation of Schottky barrier junctions and current conduction in TiO(x)-based devices under various biasing polarities. Introduction of the Pt midlayer creates two additional Schottky barriers, which mediate the band bending potential at each metal-oxide interface and attains a rectifying current conduction at the high-resistance state. The rectifying conduction behavior is also observed with an AFM-tip as the top electrode, which implies the rectifying property is still valid when miniaturizing the device to nanometer scale. The current rectification consequently leads to a single-polarity, unipolar resistive switching and electrically rewritable performance for the TiO(x)/Pt/TiO(x) device.