The memristor is a promising candidate to implement high-density memory and neuromorphic computing. Based on the characteristic retention time, memristors are classified into volatile and non-volatile types. However, a single memristor generally provides a specific function based on electronic performances, which poses roadblocks for further developing novel circuits. Versatile memristors exhibiting both volatile and non-volatile properties can provide multiple functions covering non-volatile memory and neuromorphic computing. In this work, a versatile memristor with volatile/non-volatile bifunctional properties was developed. Non-volatile functionality with a storage window of 4.0 × 105 was obtained. Meanwhile, the device can provide threshold volatile functionalities with a storage window of 7.0 × 104 and a rectification ratio of 4.0 × 104. The leaky integrate-and-fire (LIF) neuron model and artificial synapse based on the device have been studied. Such a versatile memristor enables non-volatile memory, selectors, artificial neurons, and artificial synapses, which will provide advantages regarding circuit simplification, fabrication processes, and manufacturing costs.