This paper is concerned with the issue of adaptive synchronization for a general class of chaotic memristive competitive neural networks (MCNNs) with mixed time-varying delays and different time scales.By applying Lyapunov functional method and inequality analysis technique,a kind of novel adaptive controllers with feedback control laws are designed to achieve synchronization and exponential synchronization.The synchronization conditions,without need of excessive calculation such as solving linear matrix inequality or computing algebraic conditions,are given,which can be applied in MCNNs with different mathematical models of memristor proposed in the existing literature.Finally,an example with numerical simulations is listed to prove the efficiency and accuracy of the theoretical results.