It is known that graphene nanoribbon (GNR) based devices and interconnects can be treated to be better alternative in nano-scale designs. In this paper, given a source pin and a set of target pins inside a GNR grid-based routing plane, based on the consideration of the wirelength and bending delay in graphene nanoribbon, an efficient routing algorithm can be proposed to construct a delay-driven GNR routing tree with minimizing the total wirelength for the target pins. Compared with Das's algorithm [9] on total wirelength and maximum source-to-target delay, the experimental results show that our proposed routing algorithm only uses 8.05% of the extra wirelength to reduce 23.13% of the maximum delay in the construction of a delay-driven GNR routing tree for 6 tested examples on the average.