Conventional CMOS devices are facing an increasing number of challenges as their feature sizes scale down. Graphene nanoribbon (GNR) based devices are shown to be a promising replacement of traditional CMOS at future technology nodes. However, all previous works on GNRs focus at the device level. In order to integrate these devices into electronic systems, routing becomes a key issue. In this paper, the GNR routing problem is studied for the first time. We formulate the GNR routing problem as a minimum hybrid-cost shortest path problem on triangular mesh ("hybrid" means that we need to consider both the length and the bending of the routing path). In order to model this hybrid-cost problem, we apply graph expansion and introduce a shortest red-black path problem on the expanded graph. We then propose an algorithm that solves the shortest red-black path problem optimally. This algorithm is then used in a negotiated congestion based routing scheme. Experimental results show that our GNR routing algorithm effectively handles the hybrid cost.