Events describe the state changes of entities. In a document, multiple events are connected by various relations (e.g., Coreference, Temporal, Causal, and Subevent). Therefore, obtaining the connections between events through Event-Event Relation Extraction (ERE) is critical to understand natural language. There are two main problems in the current ERE works: a. Only embeddings of the event triggers are used for event feature representation, ignoring event arguments (e.g., time, place, person, etc.) and their structure within the event. b. The interconnection between relations (e.g., temporal and causal relations usually interact with each other ) is ignored. To solve the above problems, this paper proposes a jointly multiple ERE framework called GraphERE based on Graph-enhanced Event Embeddings. First, we enrich the event embeddings with event argument and structure features by using static AMR graphs and IE graphs; Then, to jointly extract multiple event relations, we use Node Transformer and construct Task-specific Dynamic Event Graphs for each type of relation. Finally, we used a multi-task learning strategy to train the whole framework. Experimental results on the latest MAVEN-ERE dataset validate that GraphERE significantly outperforms existing methods. Further analyses indicate the effectiveness of the graph-enhanced event embeddings and the joint extraction strategy.