Electronic medical records (EMRs) contain a variety of valuable medical entities and their relations. The extraction of medical entities and their relations has important application value in the structuring of EMR and the development of various types of intelligent assistant medical systems, and hence is a hot issue in intelligent medicine research. In recent years, most research aims to firstly identify entities and then to recognize the relations between the entities, and often suffers from many redundant operations. Furthermore, the challenge remains of identifying overlapping relation triplets along with the entire medical entity boundary and detecting multi-type relations. In this work, we propose a Specific Relation Attention-guided Graph Neural Networks (SRAGNNs) model to jointly extract entities and their relations in Chinese EMR, which uses sentence information and attention-guided graph neural networks to perceive the features of every relation in a sentence and then to extract those relations. In addition, a specific sentence representation is constructed for every relation, and sequence labeling is performed to extract its corresponding head and tail entities. Experiments on a medical evaluation dataset and a manually labeled Chinese EMR dataset show that our model improves the performance of Chinese medical entities and relation extraction.