Summary: A class of Cohen-Grossberg neutral networks (CGNNs) with time-varying delays on time scales is considered. We establish some sufficient conditions on the existence and exponential stability of anti-periodic solutions for CGNNs $$x^Δ_i(t)=-a_i(x_i(t))\left[b_i(x_i(t))-\sum^n_{j=1}c_{ij}(t)f_j(x_j(t))-\sum^n_{j=1}d_{ij}(t) f_j(x_j(t-τ_{ij}(t)))+I_i(t)\right],$$ where $t\in{\bbfT}$, $T$ is a periodic time scale, $i=1,2,\dots,n$.