The ecological aspect of substituting synthetic materials with natural materials is of great interest nowadays. This paper examines the percentage of lignocellulose-based fillers that can be added to a synthetic polymer matrix to ensure the resulting biocomposite maintains its dielectric properties. Biocomposites were made from isotactic polypropylene (iPP) and various proportions (20%, 30%, and 40%) of oats, rye, wheat, and barley bran and granules from corn cobs using a Brabender plastograph and a hydraulic hot press. From a morphological analysis, it was noted that the particles were well incorporated into the polymer matrix. The frequency-dependent behavior of the dielectric properties was analyzed across a frequency range from 30 Hz to 60 kHz at a room temperature of 23 °C and 35% relative humidity. The obtained results showed that the incorporation of biomasses into the iPP matrix increased the values of the dielectric properties across the entire measured frequency range. The samples with wheat showed the most stable values of the dielectric parameters with frequency changes, for all three concentrations. A linear regression analysis showed a very high coefficient of determination (R² = 0.997) between the effective dielectric permeability and filler concentration at 30 Hz for the samples with wheat. Furthermore, the biocomposite iPP/20% wheat showed a desirable balance of dielectric properties for electronic applications. The results showed that biocomposites obtained by adding cheap lignocellulose-based biomass, such as bran or granules from corn cobs, to a synthetic polymer matrix have a great potential for use as electrically insulating materials because their dielectric parameters are comparable to those of standard insulating materials.