In this paper, the passivity problem of memristor-based recurrent neural networks (MRNNs) with mixed time-varying delays is investigated. We adopt a switched system to describe the memristor-based recurrent neural network with mixed time-varying delays. By constructing appropriate Lyapunov-Krasovski functionals, two sufficient conditions for passivity and exponential passivity of MRNNs are established in terms of linear matrix inequalities (LMIs), respectively. An example is given to demonstrate the effectiveness of the obtained results.