In this paper, a new type of neural networks, quaternion-valued memristive neural networks (QVMNNs) is formulated. On the basis of the differential inclusion principle and the Lyapunov functional method, fixed-time synchronization problem is considered in the form of drive-response system for this type of neural networks. A novel fixed-time controller is designed to achieve the control goal. With the fixed-time stability theory and some inequality techniques, criterion of fixed-time synchronization for QVMNNs is given. Finally, corresponding simulation results are presented to show the effectiveness of the method derived in this paper.