Perfect graphene is believed to be the strongest material. However, the useful strength of large-area graphene with engineering relevance is usually determined by its fracture toughness, rather than the intrinsic strength that governs a uniform breaking of atomic bonds in perfect graphene. To date, the fracture toughness of graphene has not been measured. Here we report an in situ tensile testing of suspended graphene using a nanomechanical device in a scanning electron microscope. During tensile loading, the pre-cracked graphene sample fractures in a brittle manner with sharp edges, at a breaking stress substantially lower than the intrinsic strength of graphene. Our combined experiment and modelling verify the applicability of the classic Griffith theory of brittle fracture to graphene. The fracture toughness of graphene is measured as the critical stress intensity factor of and the equivalent critical strain energy release rate of 15.9 J m-2. Our work quantifies the essential fracture properties of graphene and provides mechanistic insights into the mechanical failure of graphene.