The tunneling magneto-dielectric (TMD) effect, which causes a magnetic field-induced increase in the dielectric permittivity (ϵ′0) of nanogranular films, is promising for use in multifunctional devices. However, the frequency response of the TMD effect features a peak dielectric change (the TMD ratio, Δϵ′/ϵ′0) at a specific frequency, which inevitably limits the utility of the effect to within a narrow frequency range. To achieve the high TMD effect over a wider frequency band, we experimentally and theoretically report composition-graded multilayer (CGM) Co-MgF2 nanogranular films (i.e., with a step-varied granular Co content) with still high TMD ratios beyond this particular frequency range. Theoretical fittings of the experimental dielectric and TMD results indicate that the wide inter-granular spacing distribution in CGM films represents the origin of the broadband TMD effect. This study clarifies the critical role of the granular distribution in regulating the frequency response of the TMD properties. The proposed CGM structure, which can go beyond the limitations of conventional uniform nanogranular materials, will enable broadband magnetoelectric device applications of the TMD effect.