Giant dielectric behavior and electrical properties of monovalent cation/anion (Li+, F-) co-doped CaCu3Ti4O12 ceramics prepared by a solid-state reaction route were systematically investigated. Substitution of Li+ and F- led to a significantly enlarged mean grain size. A reduced loss tangent (tan delta similar to 0.06) with the retainment of an ultra-high dielectric permittivity (epsilon ' similar to 7.7-8.8 x 10(4)) was achieved in the co-doped ceramics, while the breakdown electric field and nonlinear coefficient of CaCu3Ti4O12 ceramics were increased by co-doping with (Li+, F-). The variations in nonlinear electrical properties and giant dielectric response, as well as the dielectric relaxation, were well explained by the Maxwell-Wagner polarization model for an electrically heterogeneous microstructure, in which a Schottky barrier height at the grain boundaries (GBs) was formed. epsilon ' was closely correlated to the GB capacitance. Significantly decreased tan delta value and enhanced nonlinear properties were related to a significant increase in the GB resistance, which was attributed to the significantly increased potential barrier height and conduction activation energy at the GBs. The semiconducting nature of the grains was also studied using X-ray photoelectron spectroscopy and found to originate from the presence of Cu+ and Ti3+ ions.