In tunable filters, the passband frequency can be effectively tuned via mechanical, [2,3] magnetic, [4,5] or electrical approaches, [6] and have been explored using a variety of technologies, including switched capacitor networks, [7] microelectromechanical systems, [8] ferroelectric, [9] and ferromagnetic films. [4] Tunable frequency filters may cover multiple frequencies to meet different scenarios in multiple band operations.Nanogranular materials comprise disordered nanometer-sized granular metals dispersed in a host matrix and are a robust platform for studying complex disordered solids. [10,11] Based on this platform, a variety of intriguing phenomena have been discovered that involve the interplay of electronic, [12,13] magnetic, [14,15] optical, [16,17] and thermal properties, [18,19] as well as quantum [20] and superconductive behavior. [21] At diluted granular fractions (typically less than the percolation threshold of 50 vol%), the materials are in the dielectric regime, whereby both DC [22,23] and AC [24,25,26,27] electrical transport properties have been widely studied in this regime. In particular, the study of AC transport provides an in-depth understanding of the electric polarization associatedThe electrical modulation of the functionality of matter is of significant interest in physics and multifunctional tunable electronic device applications.Here, new dielectric materials with nanogranular structures comprised of nano-sized Co granular metals dispersed in a Mg-fluoride-based dielectric matrix are explored. The dielectric relaxation frequency (f r ), which represents a sharp decrease in dielectric permittivity in dielectrics, can be tuned by a DC electric field (E). As E increases, the position of f r first shifts to the lowfrequency side and then to the high-frequency side, achieving a tunable f r in a certain frequency range. The ability to electrically modulate the relaxation frequency may help construct novel tunable frequency filters. The dielectric properties are theoretically examined based on the asymmetric electron tunnelling model that considers the size difference of granular pairs, offering an insightful understanding of the structure-property relationship in disordered granular solids.