TCP unfairness is a critical problem in Wireless Mesh Network. Fair TCP services with high quality are difficult to obtain. While modeling for the related protocols of different layers will greatly help us analyze the active factors of TCP fair transmission and come up with better protocol design for Wireless Mesh Network. The state transitions of MAC and TCP were modeling based on Markov chain in typical IEEE 802.11b/g based Wireless Mesh Network. Then, the TCP delay and throughput were analyzed based on the modeling. The contrast between simulation results and theoretic values of delay and throughput proves that the modeling and analyzing are correct. The important influence factors found are helpful for research on TCP fairness in Wireless Mesh Network.