Graphene, a new material with a hexagonal honeycomb sheet structure composed of a single layer of carbon atoms, is the world's thinnest and strongest substance known to human, it has low resistivity and strong light transmission characteristics, so it can be used as a candidate material for integrated circuit chips and new energy batteries. In this paper, we mainly discuss the quantum walk of two non-interacting particles on the graphene structure graph, in which we select coin operator G in coin space HC and construct shift operator S, the time evolution operator U is obtained from the tensor of G and S. Since two particles without interaction can occupy the same site, the initial state is a composite of two particles at the same site. On this foundation, the relation between the relative distance and evolution time of two non-interacting particles is studied by the distance evolution operator.