In this paper we study the Forest Wrapping Problem (FWP) which can be stated as follows: given a connected graph G = (V,E), with ∣V ∣ = n, let π₀ be a partition of G into K (not necessarily connected) components, find a connected partition π^* of G that wraps π₀ and has maximum number of components. The Forest Wrapping problem is NP-complete on grid graphs while is solvable in O(n log n) time on ladder graphs. We provide a two-phase O(n ² ) time algorithm for solving FWP on outerplanar graphs.