In this work we have studied the evolution of a warped product (WP) manifold under second orderrenormalization group (RG-2) flow. We have shown some conditions for the existence of a solution of RG-2flow on WP manifolds. Also, we have found a necessary condition for warped function under RG-2 flow. Inparticular, we study some special WP metric of real line with a manifold. Eventually, by extending conditionsto pseudo-Riemannian manifold, we find a PDE for Robertson-Walker (RW) metrics, and show that there isno RG-2 flow for RW metrics.