The discovery of a giant dielectric constant(1-3) of 10(5) in CaCu3Ti4O12 has increased interest in this perovskite-type oxide. Here we demonstrate that, in addition to high permittivity, CaCu3Ti4O12 has remarkably strong nonlinear current-voltage characteristics without the addition of any dopants. An intrinsic electrostatic barrier at the grain boundaries is responsible for the unusual nonlinear behaviour. The nonlinear coefficient of CaCu3Ti4O12 reaches a value of 900, which is even greater than that of the varistor material(4) ZnO. As a result, CaCu3Ti4O12 may lead to efficient switching and gas-sensing devices.