This article presents an efficient TSK-type recurrent fuzzy cerebellar model articulation controller (T-RFCMAC) model based on a dynamic-group--based hybrid evolutionary algorithm (DGHEA) for solving identification and prediction problems. The proposed T-RFCMAC model is based on the traditional CMAC model and the Takagi--Sugeno--Kang (TSK) parametric fuzzy inference system. Otherwise, the recurrent network, which imports feedback links with a receptive field cell, is embedded in the T-RFCMAC model, and the feedback units are used as memory elements. The DGHEA, which is a hybrid of the dynamic-group quantum particle swarm optimization (QPSO) and the Nelder--Mead method, is proposed for adjusting the parameters of the T-RFCMAC model. In DGHEA, an entropy-based grouping technique is adopted to improve the searching capability and the convergent speed of quantum particles swarm optimization. Experimental results show that the proposed DGHEA-based T-RFCMAC model is more effective at identification and prediction than other models.