With the electronic equipment becoming more integrated, multifunctional and lightweight, the demand for advanced thermal management materials with excellent electrical insulation and high thermal conductivity is increasing. In this study, the fluorographene (FG) nanosheets with different degrees of fluorination were successfully exfoliated from the corresponding raw graphite fluoride by using a facile low-energy ball milling process and ultrasonic treatment. And then ethylene vinyl acetate copolymer/fluorographene (EVA/FG) composite films were prepared by a knife coating method. The effects of fluorination degree and content of FG on the thermal conductivity and electrical insulation of FG composites were systematically studied. An in-plane thermal conductivity of 52.9 W m-1 K -1 and through-plane thermal conductivity of 2.5 W m-1 K -1 have been achieved in the prepared composite films with the FG content of 70 wt% and the C:F ratio of 1:0.63. The prepared composite films also show excellent thermal stability to withstand the repeated cooling and heating, as well as high electrical insulation and good flexibility, which makes the FG composites be of great potential usage in the field of intelligent wearable devices, soft robots, flexible electronics and so on.