Abstract: This paper studies the exponential stability of a class of quaternion-valued neural networks with time-varying delays. The concerned quaternion-valued models were separated into four real-valued parts to form the equivalent real-valued systems. It was assumed that the activation functions were strong-coupled. Based on M-matrix properties and vector Lyapunov function method, the exponential stability of the equilibrium point of the system was analyzed, and the corresponding stability conditions were obtained for ensuring the exponential stability of the system, which was in form of compact and easy to be verified in practice. The obtained results in this paper complement the existing ones, and are the less level conservatism compared to the existing ones. Finally, a numerical example was provided to illustrate the correctness and the less level conservatism of the main results.