Memristors are considered a very important component to build artificial neural networks and realize logic-inmemory computing that could revolutionize current von Neumann computing architectures. With a significant resistance switching behavior, memristor has ability of simulating neuromorphic computing in human brain. However, the development of memristor is restricted by reliability, manufacturing consistency, and fundamental mechanisms. To conquer these problems, a longterm stable device, the high-quality deposition method, and the investigation on the mechanism are required. In this work, a memristor with an asymmetric-resistive-switching (ARS) behavior was fabricated via the sputtering method, which is based on the structure of Mo/ZnO/In-doped Tin Oxide (ITO). It presented a unique voltage-controlled resistance switching behavior with multistate, which has long-term endurance and low volatility. It demonstrates long-term potentiation and depression characteristics. The mechanism of the unique ARS behavior was discussed. The ARS behavior could realize coupled AND and OR logic-in-memory operation. This device provides a promising application in the complex integrated circuits and artificial intelligence.