In this paper, we consider the problem of existence of almost periodic solutions of impulsive Cohen-Grossberg neural networks with time-varying delays. The impulses are not at fixed moments, but are realized when the integral curves of solutions meet given hypersurfaces, i.e., the investigated model is with variable impulsive perturbations. Sufficient conditions for perfect stability of almost periodic solutions are derived. The main results are obtained by employing the Lyapunov-Razumikhin method and a comparison principle. In addition, the obtained results are extended to the uncertain case, and robust stability of almost periodic solutions is also investigated. An example is considered to demonstrate the effectiveness of our results.