We have devised a method to selectively fluorinate graphene by irradiating fluoropolymer-covered graphene with a laser. This fluoropolymer produces active fluorine radicals under laser irradiation that react with graphene but only in the laser-irradiated region. The kinetics of C-F bond formation is dependent on both the laser power and fluoropolymer thickness, proving that fluorination occurs by the decomposition of the fluoropolymer. Fluorination leads to a dramatic increase in the resistance of the graphene while the basic skeletal structure of the carbon bonding network is maintained. Considering the simplicity of the fluorination process and that it allows patterning with a nontoxic fluoropolymer as a solid source, this method could find application to generate fluorinated graphene in graphene-based electronic devices such as for the electrical isolation of graphene.