For the use in low-power and lossy networks (LLNs) under complex and harsh communication conditions, the routing protocol for LLNs (RPL) standardized by the Internet Engineering Task Force is specially designed. To improve the performance of LLNs, we propose a novel context-aware RPL algorithm based on a triangle module operator (CAR-TMO). A novel composite context-aware routing metric (CA-RM) is designed, which synchronously evaluates the residual energy index, buffer occupancy ratio of a node, expected transmission count (ETX), delay, and hop count from a candidate parent to the root. CA-RM considers the residual energy index and buffer occupancy ratio of the candidate parent and its preferred parent in a recursive manner to reduce the effect of upstream parents, since farther paths are considered. CA-RM comprehensively uses the sum, mean, and standard deviation values of ETX and delay of links in a path to ensure a better performance. Moreover, in CAR-TMO, the membership function of each routing metric is designed. Then, a comprehensive membership function is constructed based on a triangle module operator, the membership function of each routing metric, and a comprehensive context-aware objective function. A novel mechanism for calculating the node rank and the mechanisms for preferred parent selection are proposed. Finally, theoretical analysis and simulation results show that CAR-TMO outperforms several state-of-the-art RPL algorithms in terms of the packet delivery ratio and energy efficiency.