This study proposes a group information recommendation (GIR) model to accurately and comprehensively explore group preferences and enhances complex groups' recommendation effect. Firstly, the group recommendation (GR) algorithm, Multi-Head Attention (MHA) mechanism, and Graph Neural Network (GNN) are summarized. Secondly, the GIR model is constructed using the MHA and GNN models. On the one hand, the model considers the importance of differences in group objects' preferences in different item recommendations. On the other hand, the impact of the interaction between objects on group preference modeling is considered. The constructed GIR model includes an embedding layer, a propagation layer, a fusion layer, and a prediction layer. Finally, experiments are conducted to verify the effectiveness of the constructed model. The verification results reveal that: (1) compared with other recommendation models, the Multi-Head Attention-Graph Neural Network (MHA-GNN) model is improved by 1.05% in the Mean Reciprocal Rank (MRR) index. (2) The recommendation precision and MRR value of the MHA-GNN model are higher than those of other fused models. (3) Compared with other recommendation models, the MHA-GNN model has the highest recommendation precision and better recommendation effect. The above conclusions show that the introduced GNN technology can effectively improve the performance of the GR model. At the same time, the established GIR system has a more accurate recommendation effect, which can realize the efficient mining of group preferences. This study aims to achieve the efficient recommendation of information and save information retrieval time.