To satisfy requirements from various applications in the smart grid, transmitting data robustly and reliably has become one of the most crucial tasks. However, existing routing protocols like CTP, LEACH, HWMP cannot be directly applied to the smart grid system. In this paper, we propose RH-HWMP, which provides robust data transmission for the neighbor area network (NAN) in the smart grid. The main idea of RH-HWMP is to utilize a greedy path selection algorithm to select backup paths with minimum fault dependence based on the reliability history of links. Once the first priority path fails, the node switches to the backup path immediately, which can efficiently improve robustness and fault tolerance of the network. We simulate RH-HWMP with NS-3, and the results demonstrate that RH-HWMP can improve the robustness of the network with limited overhead compared with traditional routing protocol HWMP.