This paper addresses the multistability issue for quaternion-valued neural networks (QVNNs) with time delays. By using the inequality technique, sufficient conditions are proposed for the boundedness and the global attractivity of delayed QVNNs. Based on the geometrical properties of the activation functions, several criteria are obtained to ensure the existence of 81n equilibrium points, 16n of which are locally stable. Two numerical examples are provided to illustrate the effectiveness of the obtained results.