This paper presents the exponential synchronization for a class of memristive Cohen-Grossberg neural networks (MCGNNs) with mixed delays via a new hybrid control strategy. This new hybrid control strategy combines pinning control and periodic intermittent control. According to the feature of memristor, the memristive terms of the MCGNNs with mixed delays are normalized by a simple linear transformation. Then the designed periodic intermittent control is added to selected partial network nodes. Based on the stability theory of memristive neural networks and the exponential synchronization rule, the new synchronization conditions are given. Finally, numerical simulations are provided to show the effectiveness of the theoretical method.