We studied the reactivity of finite-sized graphene with methyne (CH radical) theoretically by means of density functional theory (DFT) calculations. We identified a favorable reaction site for model graphene by comparing the total energies of the adducts corresponding to the inequivalent reaction sites. The addition of methyne to an edge site of the graphene was energetically favorable rather than an inner site. The potential energy barrier for the methyne addition became lower as the model size became larger. We also discuss the reactivity of methyne with graphene discussed on the basis of our calculation results.