Graphene sheet/polymeric carbon nitride nanocomposite (GSCN) functions as a metal-free catalyst to activate O-2 for the selective oxidation of secondary C-H bonds of cyclohexane. By fine-tuning the weight ratio of graphene and carbon nitride components, GSCN offers good conversion and high selectivity to corresponding ketones. Besides its high stability, this catalyst also exhibits high chemoselectivity for secondary C-H bonds of various saturated alkanes and, therefore, should be useful in overcoming challenges confronted by metal-mediated catalysis.