Graphene is generally used for conductive material; it can also be used as a key nanofiller for the insulation material of inverter motors. In this study, a series of polyimide (PI) films were prepared successfully by a conventional two-step polymerization method based on bis[3,5-dimethyl-4-(4-aminophenoxy)phenyl]methane as a diamine and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride as a dihydride with different weight percentage graphene oxide (GO) nanosheets as nanofillers. The dielectric constant (ε) and dielectric loss (tan δ) of these films were measured. The results show good dielectric properties, especially an ultralow ε value of 1.41 at 1 MHz with 0.19% GO. This showed that the low ε value was caused by a high free volume led by the GO nanosheets and the CF bond. The structure and micromorphology of the PIs were characterized by X-ray diffraction and scanning electron microscopy. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41385.