This paper mainly deals with the adaptive synchronization problem of memristor-based complex-valued neural networks with time delays. In order to make the system itself adjust to achieve stable synchronization, the concept of adaptive control technology is used, a specific feedback controller is designed to achieve synchronization. The obtained results are more reliable and improve some existing achievements on the synchronization of real-valued memristor-based neural networks. Two numerical examples are given to illustrate the effectiveness of the theoretical results.