Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind in [5] to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical geometry. In this article, we present a theory of Gröbner bases for polytopal affinoid algebras that extends both Caruso et al.’s theory of Gröbner bases on Tate algebras of [1] and Pauer et al.’s theory of Gröbner bases on Laurent polynomials of [9].