Aiming at the channel allocation problem caused by the wireless Access Points (APs) in Multiple Input Multiple Output (MIMO) Wireless Local Area Network (WLAN) when accessing to the Television White Space (TVWS) authorized frequency band in cognitive way, this paper firstly models the Primary User (PU) and secondary user's network interference based on MIMO channel. Also, the number of accessed secondary users under PU outage probability is deduced. Then, by modeling the channel interference among Basic Service Set (BSS) where secondary users exist, the mutual interference degree among APs and the actual throughput of the cognitive network are analyzed. Secondly, under the premise of guaranteeing the PU Quality of Service (QoS) and ensuring the secondary users QoS ultimately, this paper models the channel allocation problem as a nonlinear integer programming problem. Besides, the optimal allocation of the secondary user channels and the transmit power are obtained according to Karush-Kuhn-Tucker (KKT) theory and Water-Filling method. Numerical analysis results verify the rationality and the validity of the proposed channel allocation algorithm in terms of the total channel capacity of cognitive network and load balancing among BSS.