We report the extreme sensitivity of dielectric permittivity to applied dc bias electric field in bulk LuFe2O4. A small bias field of 50 V/cm can greatly reduce the dielectric permittivity in the vicinity of room temperature, which is in strong contrast to conventional ferroelectric materials where a large electric field of the order of tens of kV/cm is required. This giant dielectric tunability effect within a broad temperature interval around room temperature is very promising for tunable device applications. The possible origins of this giant effect are discussed.