This article introduces a kind of composite material made of kapok fibre and polycaprolactone by the hot-pressing method. The effects of volume density, mass fraction of kapok fibre, and thickness on the sound-absorption performance of composites were researched using a single-factor experiment. The sound-absorption performance of the composites was investigated by the transfer function method. Under the optimal process parameters, when the density of the composite material was 0.172 g/cm3, the mass fraction of kapok was 40%, and the thickness was 2 cm, the composite material reached the maximum sound-absorption coefficient of 0.830, and when the sound-absorption frequency was 6300 Hz, the average sound-absorption coefficient was 0.520, and the sound-absorption band was wide. This research used the box dimension method to calculate composites’ fractal dimensions by using the Matlab program based on the fractal theory. It analysed the relationships between fractal dimension and volume density, fractal dimension and mass fraction of kapok fibre, and fractal dimension and thickness. The quantitative relations between fractal dimension and maximum sound-absorption coefficient, fractal dimension, and resonant sound-absorption frequency were derived, which provided a theoretical basis for studying sound-absorption performance. The results showed that kapok fibre/polycaprolactone composites had strong fractal characteristics, which had important guiding significance for the sound-absorption performance of kapok fibre composites.