In this paper we study an induced L(2) norm model reduction problem for polytopic uncertain linear systems. The polytopic system has its state-space data contained in a convex polytope, a situation which often arises. The problem we address is to approximate this type of system by a lower order polytopic uncertain linear system with a guaranteed induced L(2) norm error. A sufficient solvability condition is provided in terms of LMIs with one extra coupling rank constraint, which generally leads to a nonconvex feasibility problem. We use an improved computational scheme based on the alternating projection method to obtain solutions to the problem, but only local convergence is guaranteed. The reduced-order uncertain system with its associated polytope is given explicitly by the solution of the feasibility problem.