A giant dielectric tunability effect in LuFe2O4 was recently discovered by our group. Here we report the influence of Mg doping on the dielectric tunability and dielectric loss in LuFe2-xMgxO4 (x <= 0.1) samples. It was found that the temperature interval of the giant dielectric tunability is broadened by a slight (5%) Mg doping, while the dielectric loss remains the same order. The maximum value of tunability is reduced by Mg doping, which supports the viewpoint that the giant dielectric tunability is crucially related to charge ordering of Fe2+ and Fe3+ ions. These results suggest that the giant dielectric tunability in LuFe2O4 can be finely tuned by Mg doping.