The Fermi velocity, v_F, is one of the key concepts in the study of a material, as it bears information on a variety of fundamental properties. Upon increasing demand on the device applications, graphene is viewed as a prototypical system for engineering v_F. Indeed, several efforts have succeeded in modifying v_F by varying charge carrier concentration, n. Here we present a powerful but simple new way to engineer v_F while holding n constant. We find that when the environment embedding graphene is modified, the v_F of graphene is (i) inversely proportional to its dielectric constant, reaching v_F ~ 2.5×10⁶ m/s, the highest value for graphene on any substrate studied so far and (ii) clearly distinguished from an ordinary Fermi liquid. The method demonstrated here provides a new route toward Fermi velocity engineering in a variety of two-dimensional electron systems including topological insulators.