Providing per node throughput fairness is an important challenge for Wireless Mesh Networks (WMNs) in order to achieve serviceability of the entire system. However, existing protocols provide poor performance results for nodes located more than one hop away from the gateways when the network load increases. In some cases, single-hop nodes dominate the network causing throughput starvations to multi-hop nodes. In this paper, we propose a novel and efficient Mesh Fairness Algorithm (MFA) to provide per node throughput fairness with very simple-state information that considers the packets' owners and the parents activity. Our key techniques for MAC coordination is that each node adjust its backoff counter based on activities of its parent and children. Additionally, we utilize scheduling model to establish a benchmark and compare our result with the developed benchmark. The simulation results indicate that the MFA provides per node throughput fairness in a single-branch of mesh networks with a small amount of network throughput degradation and packet overhead.