Electrochemical nanomaterial-based resistive switching devices (memristors) have recently attracted significant research interest because of their low cost and potential applications in nonvolatile data storage and artificial neural networks. In this paper, we report an electrochemical method to produce a novel memristor based on copper nanowire-titanium dioxide nanotube arrays (TNTAs), a core-shell composite material. TNTAs are fabricated using a cheap and effective electrochemical anodization method, and high-density copper nanowires are synthesized via excess-electrodeposition with a novel peeling-off strategy. This novel memristor shows both analogue and digital resistive switching properties by controlling the electroforming process. The Roff/Ron ratio of the digital memristor remains greater than 40 during 1000 consecutive I–V sweeps. The device shows good endurance over 104 pulse cycles, with an Roff/Ron ratio greater than 20. Furthermore, the data retention time can be maintained at least for 104 s. The outstanding digital resistive switching performance can be attributed to the numerous parallel copper nanowire nanoelectrodes inside the film.