Pre-trained wav2vec2.0 model has been proved its effectiveness for speaker recognition. However, current feature processing methods are focusing on classical pooling on the output features of the pre-trained wav2vec2.0 model, such as mean pooling, max pooling etc. That methods take the features as the independent and irrelevant units, ignoring the inter-relationship among all the features, and do not take the features as an overall representation of a speaker. Gated Recurrent Unit (GRU), as a feature fusion method, can also be considered as a complicated pooling technique, mainly focuses on the temporal information, which may show poor performance in some situations that the main information is not on the temporal dimension. In this paper, we investigate the graph neural network (GNN) as a backend processing module based on wav2vec2.0 framework to provide a solution for the mentioned matters. The GNN takes all the output features as the graph signal data and extracts the related graph structure information of features for speaker recognition. Specifically, we first give a simple proof that the GNN feature fusion method can outperform than the mean, max, random pooling methods and so on theoretically. Then, we model the output features of wav2vec2.0 as the vertices of a graph, and construct the graph adjacency matrix by graph attention network (GAT). Finally, we follow the message passing neural network (MPNN) to design our message function, vertex update function and readout function to transform the speaker features into the graph features. The experiments show our performance can provide a relative improvement compared to the baseline methods. Code is available at xxx.