The existence and the S-asymptotic $\omega$-periodic of the solution in fractional-order Cohen-Grossberg neural networks with inertia are studied in this paper. Based on the properties of the Riemann-Liouville (R-L) fractional-order derivative and integral, the contraction mapping principle, and the Arzela-Ascoli theorem, sufficient conditions for the existence and the S-asymptotic $\omega$-period of the system are achieved. In addition, an example is simulated to testify the theorem.