In LLNs, not only the transmission qualities between a sender and a receiver, but also the channel contention and resource limitations at the receiver side should be considered. In wireless sensors networks the Medium Access Control protocol CSMA/CA uses Binary Exponential Backoff algorithm (BEB) to address the channel collision problem. Though BEB reduces collision on the multiple channel access, there is still a high packet drop probability due to the buffer limitation on the receiving node. In this paper, we focus on the BEB issues for RPL networks which is a one of the most popular cooperative routing protocols in WSN. In RPL, it is not uncommon to have a node with relatively higher traffic than neighbor nodes because children nodes have a tendency to select a good routing metric node as a parent. If traffic concentrates on a good quality parent, it becomes inevitable to get packet loss due to the buffer overflow and channel collision. Nodes are cooperative to achieve common goals instead of competing each other in RPL. In such environment, the throughput may be much more important criteria than fairness. We propose a Traffic-aware Cooperative BEB algorithm (TBEB) for RPL networks which handles the multiple channel access issue in such a way that it avoids not only the collision at the sender (child node) side but also the buffer overflow at the receiver (parent node) side without degrading the channel utilization and the throughput efficiency. Simulation results show that the TBEB algorithm can reduce the channel collision while maintaining good channel utilization and reduction in packet drop counts resulted from buffer overflow.