Annotation conversion is an effective way to construct datasets under new annotation guidelines based on existing datasets with little human labour. Previous work has been limited in conversion between tree-structured datasets and mainly focused on feature-based models which are not easily applicable to new conversions. In this paper, we propose two simple and effective graph-to-graph annotation conversion approaches, namely Label Switching and Graph2Graph Linear Transformation, which use pseudo data and inherit parameters to guide graph conversions respectively. These methods are able to deal with conversion between graph-structured annotations and require no manually designed features. To verify their effectiveness, we manually construct a graph-structured parallel annotated dataset and evaluate the proposed approaches on it as well as other existing parallel annotated datasets. Experimental results show that the proposed approaches outperform strong baselines with higher conversion score. To further validate the quality of converted graphs, we utilize them to train the target parser and find graphs generated by our approaches lead to higher parsing score than those generated by the baselines.