In this paper, we study the existence of weighted pseudo-almost periodic solutions and the global exponential synchronization of delayed quaternion-valued cellular neural networks (QVCNNs). Firstly, we use the Banach fixed point theorem to establish the existence of weighted pseudo-almost periodic solutions for this class of QVCNNs. Then, under the condition that the drive system has a unique weighted pseudo-almost periodic solution, by designing a state-feedback controller and constructing suitable Lyapunov functions, we see that the drive-response structure of delayed QVCNNs with weighted pseudo-almost periodic coefficients achieve global exponential synchronization. Finally, a numerical example is given to illustrate the feasibility of our results.