Memristors have great application in many fields such as neural networks, non-volatile memory and nonlinear circuits by virtue of the nanoscale and non-volatile characteristics. Multi-valued devices possess significant meaning in digital logic circuit, chaos control and synapse networks. In this paper, the concept of multi-valued memristors is proposed, and the ternary voltage-controlled memristor is taken as an example investigated concretely. Moreover, the specific ternary mathematical model is given and a series of numerical analyses have been studied. After that, a ternary voltage-controlled memristor emulator is realized by off-the-shelf circuit components, both Multisim simulations and hardware experiments are performed to verify its effectiveness and the results shows that the theoretical analysis based on the mathematical model is in good agreement with the simulation and experimental results, which laid the theoretical foundation for the construction of multi-valued digital logic and other multi-valued applications.