Lévy processes provide a solution to overcome the shortcomings of the lognormal hypothesis. A growing literature proposes the use of pure-jump Lévy processes such the variance-gamma model. In this setting, explicit solutions for derivative prices are unavailable, for instance for the valuation of American options. We propose a dynamic programming approach coupled with finite elements for valuing American-style options under an extended variance-gamma model. Our numerical experiments confirm the convergence and show the efficiency of the proposed methodology. We also conduct a numerical investigation that focuses on American options on the S&P 500 futures contracts.