High-dielectric constant all-organic composite films consisting of polyaniline (PANI) filler and poly(butylene succinate) host were synthesized by simple blending process. The chemical structures and morphology of the composite films were characterized by Fourier transform infrared spectroscopy and scanning electron microscopy, respectively. The dielectric properties of the composite films with different filler concentrations were studied in the frequency range of 100–106 Hz. A percolation phenomenon was observed in the composite films with a percolation threshold vc = 19.7% and the dielectric constant was 10 times that of the pure host material. The enhancement in the dielectric constant can be ascribed to Maxwell–Wagner–Sillars polarization and the low-dielectric loss to good dispersion of PANI filler in the host. As the host polymer is biodegradable, it may be applied as a “green” dielectric material.