Memristors have been highlighted as candidates for artificial synapse devices in neuromorphic computing systems, due to their analog conductance update characteristics and simple two-terminal structure. However, resistive switching in conventional memristor devices relies on stochastic filament growth and rupture, degrading the reliability of memristor devices. Here, a highly reliable memristor with a self-rectifying characteristic has been developed by designing a switching layer (TiOx) with gradual oxygen concentration for uniform non-filamentary resistive switching. The device also exhibits a diode-like self-rectifying characteristic which enables a selector-free crossbar array. Based on the highly reliable resistive switching and the self-rectifying characteristic, the uniform memristor crossbar array with 100% yield and low variation (<4%) is demonstrated.