An adaptive rate controller (ARC) based on an adaptive neural fuzzy inference system (ANFIS) is designed to autonomously adjust the data rate of a mobile heterogeneous network to adapt to the changing traffic load and the user speed for multimedia call services. The effect of user speed on the handoff rate is considered. Through simulations, it has been demonstrated that the ANFIS-ARC is able to maintain new call blocking probability and handoff failure probability of the mobile heterogeneous network below a prescribed low level over different user speeds and new call origination rates while optimizing the average throughput. It has also been shown that the mobile cognitive wireless network with the proposed CS-ANFIS-ARC protocol can support more traffic load than neural fuzzy call-admission and rate controller (NFCRC) protocol.