This article focuses on the cluster synchronization of multiple fractional-order recurrent neural networks (FNNs) with time-varying delays. Sufficient criteria are deduced for realizing cluster synchronization of multiple FNNs via a pinning control by applying an extended Halanay inequality applicable for time-delayed fractional-order differential equations. Moreover, an adaptive control applicable for the synchronization of fractional-order systems with time-varying delays is proposed, under which sufficient criteria are derived for realizing cluster synchronization of multiple FNNs with time-varying delays. Finally, two examples are presented to illustrate the effectiveness of the theoretical results.