The use of natural language processing techniques to extract events such as drug treatment and disease diagnosis from biomedical texts and the entities involved in the events, such as diseases and drugs, is important for academic research and various biomedical application systems in the field of biomedicine. At present, researchers have conducted extensive research on biomedical event extraction techniques, but there are still many challenges in the recognition of trigger words and relationship extraction of biomedical events. In this paper, we propose a joint biomedical information recognition model that incorporates external knowledge and graph convolutional neural network to address the problems of difficult recognition of abbreviations and specialized terms in biomedical texts and difficult embedding of biomedical semantic relationships. The graph convolutional neural network constructs a heterogeneous graph containing entities and semantic relations, and is able to iteratively fuse the interaction information in the local knowledge graph and the external knowledge graph to perform the task of extracting relations between biomedical entity pairs based on the obtained interaction information. After pre-training and coding, two knowledge graphs are constructed using a graph convolutional neural network to obtain feature representations of each node in the two graphs, and the two graphs are fused and iterated through the attentional entity linking method to extract the last hidden layer for final classification recognition. The UMLS is used as an external knowledge base for entity disambiguation, and the entity linker selects the corresponding entities according to the attention weights. Experiments conducted on the MLEE corpus show that the joint task is able to achieve comprehensive performance in event extraction and trigger word and element recognition.