In the era of the development of communication technologies, wireless mesh networks are introduced as an efficient and effective solution to meet user demand and service providers. In the near future, wireless mesh network technology will revolutionize the world of the next generation wireless networks. Despite the extensive studies in the field of designing such kinds of networks, it seems there are many promotions yet to be done with this technology. Wireless mesh networks includes infrastructure nodes (mesh gateway, mesh routers) and mesh users among which data are transferred to other nodes and eventually to destination. Each node in the wireless mesh network may have several wireless interfaces. Furthermore, each wireless interface can connect to different communication channels which cause inequality in the number of communication channels and wireless interfaces. one of the main challenges for the implementation of wireless mesh networks is the limited throughput capacity against the growth of the number of users. Depending on how to improve and increase the capacity of the wireless mesh networks, two approaches can be proposed; arbitrary infrastructure and random infrastructure. Since, the communication channels bandwidth of large wireless mesh network are not generally equal, the studies that analyze the throughput capacity of the wireless mesh networks are of particular importance. Studies on the throughput capacity of Multi-hop wireless networks, adhoc wireless networks and wireless mesh networks have paved the way for this research, nevertheless, a fundamental difference in modeling the conditions of the issue exist. The main context of this thesis, is studying the effect of the unequal bandwidth of communication channels on the throughput capacity of large infrastructure random wireless mesh network. To the best of our knowledge, this issue has not been addressed in the past research. This thesis is trying to find answers to the following question: By increasing the ration of the number of the communication channels and wireless interfaces, how does the asymptotic throughput capacity of the wireless mesh networks with random infrastructure change with condition of unequal bandwidth of communication channels? In this way, the asymptotic upper and lower bound of the per-client throughput capacity of network are derived. It is shown that the per-client throughput capacity is function of the network parameters. Hence, the derived bounds are tight. Keywords: Wireless Mesh Networks, Asymptotic Capacity, Throughput Capacity, Random Infrastructure