Last year, IEEE 802.11 Extremely High Throughput Study Group (EHT Study Group) was established to initiate discussions on new IEEE 802.11 features. Coordinated control methods of the access points (APs) in the wireless local area networks (WLANs) are discussed in EHT Study Group. The present study proposes a deep reinforcement learning-based channel allocation scheme using graph convolutional networks (GCNs). As a deep reinforcement learning method, we use a well-known method double deep Q-network. In densely deployed WLANs, the number of the available topologies of APs is extremely high, and thus we extract the features of the topological structures based on GCNs. We apply GCNs to a contention graph where APs within their carrier sensing ranges are connected to extract the features of carrier sensing relationships. Additionally, to improve the learning speed especially in an early stage of learning, we employ a game theory-based method to collect the training data independently of the neural network model. The simulation results indicate that the proposed method can appropriately control the channels when compared to extant methods.