The development of an accurate convolutional perfectly matched layer for the efficient termination of infinite graphene structures is introduced in this paper. Initially, the popular 2-D material receives the appropriate theoretical analysis, which reveals the necessity of a flexible terminating condition that can enhance the performance of existing absorbing schemes and offer sufficient truncation rates for the graphene's strongly confined surface waves. The consistency and behavior of the novel technique are substantiated via comprehensive comparisons with setups truncated by conventional absorbing boundary conditions. Finally, a graphene microribbon waveguide is addressed to indicate the capabilities of featured algorithm in complex structures.