We propose to use segment graph convolutional and recurrent neural networks (Seg-GCRNs), which use only word embedding and sentence syntactic dependencies, to classify relations from clinical notes without manual feature engineering. In this study, the relations between 2 medical concepts are classified by simultaneously learning representations of text segments in the context of sentence syntactic dependency: preceding, concept1, middle, concept2, and succeeding segments. Seg-GCRN was systematically evaluated on the i2b2/VA relation classification challenge datasets. Experiments show that Seg-GCRN attains state-of-the-art micro-averaged F-measure for all 3 relation categories: 0.692 for classifying medical treatment-problem relations, 0.827 for medical test-problem relations, and 0.741 for medical problem-medical problem relations. Comparison with the previous state-of-the-art segment convolutional neural network (Seg-CNN) suggests that adding syntactic dependency information helps refine medical word embedding and improves concept relation classification without manual feature engineering. Seg-GCRN can be trained efficiently for the i2b2/VA dataset on a GPU platform.