A class of incommensurate fractional-order Cohen-Grossberg neural networks with inertia was investigated in this paper. First, the sufficient conditions for the boundedness of the solutions of the system were derived using the properties of fractional-order calculus. Second, by constructing a sequence of solutions in the system and using the Ascoli-Arzela theorem, the sufficient conditions for the existence of an anti-period solution and the global asymptotical stability of the system were deduced. Finally, the correctness of theoretical reasoning results was verified by a numerical simulation.