Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group with socle H0 = 2G2(q), where q = 3f with f ⩾ 3 odd such that cd(G) = cd(H), then G is non-solvable and the chief factor G′/M of G is isomorphic to H0. If, in particular, f is coprime to 3, then G′ is isomorphic to H0 and G/Z(G) is isomorphic to H.
