Chemical vapour deposition (CVD) growth of graphene has attracted much attention, aiming at the mass production of large-area and high-quality specimens. To optimize the growth condition, CVD grown graphene is conventionally characterized after synthesis. Real-time observation during graphene growth enables us to understand the growth mechanism and control the growth more easily. Here we report the optical microscope observation of the CVD growth of graphene in real time by focusing the radiation emitted from the growing graphene, which we call 'radiation-mode optical microscopy'. We observe the growth and shrinkage of graphene in response to the switching on and off of the methane supply. Analysis of the growth feature reveals that the attachment and detachment of carbon precursors are the rate-determining factor in the CVD growth of graphene. We expect radiation-mode optical microscopy to be applicable to the other crystal growth at high temperatures in various atmospheres.