Stability is the primary concern of real-valued, complexvalued, quaternion-valued neural networks in many applications.In the case where the quaternion-valued neural networks(QVNNs) with non-differential time-varying delays is not required to be separated, the sufficiency criterion of the globalμ-stability problem for networks is proposed.By constructing the appropriate LyapunovKrasovskii functional, using the techniques of freeweight matrix and matrix inequality, the sufficient conditions for the globalμ-stability of the equilibrium point of the network under study are obtained.The linear matrix inequalities global μ-stability criterion is provided in the form of quaternionvalued linear matrix inequality (QVLMI).In addition, the results are compared with the existing results.Finally, a numerical example is also given to illustrate the validity and feasibility of the conclusion.