This paper studies the unique existence and global asymptotic stability of the equilibrium point of fractionalorder BAM neural networks, obtains the sufficient condition for the unique existence of the systematic equilibrium point by using contraction mapping principle, receives the sufficient condition of the global asymptotic stability of the equilibrium point of the studied model by constructing Lyapunov function and by using Lyapunov function theory, matrix inequality method and Laplace integral transform method, gives more strict and easier verification condition by the form of matrix inequalities and verifies the correctness of the conclusion by numerical simulation.