An edge-based high-resolution scheme for the solution of the compressible Euler equations on unstructured finite elements grids is presented. The flow solver adopted in the present work is the approximate Riemann solver developed by Roe. A high-order spatial approximation is achieved by means of a piecewise linear reconstruction of the interface variables according to the MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) formulation. Finally, non-linear limiters are introduced in order to prevent the generation of oscillations. The proposed approach corresponds with the methodology presented by Löhner in [1].