Relation extraction is a popular subtask in natural language processing (NLP). In the task of entity relation joint extraction, overlapping entities and multi-type relation extraction in overlapping triplets remain a challenging problem. The classification of relations by sharing the same probability space will ignore the correlation information among multiple relations. A relational-adaptive entity relation joint extraction model based on multi-head self-attention and densely connected graph convolution network (which is called MA-DCGCN) is proposed in the paper. In the model, the multi-head attention mechanism is specifically used to assign weights to multiple relation types among entities so as to ensure that the probability space of multiple relation is not mutually exclusive. This mechanism also predicts the strength of the relationship between various relationship types and entity pairs flexibly. The structure information of deeper level in the text graph is extracted by the densely connected graph convolution network, and the interaction information of entity relation is captured. To demonstrate the superior performance of our model, we conducted a variety of experiments on two widely used public datasets, NYT and WebNLG. Extensive results show that our model achieves state-of-the-art performance. Especially, the detection effect of overlapping triplets is significantly improved compared with the several existing mainstream methods.