Tuberculosis is a common infectious disease in the world. Tuberculosis cavities are common and important imaging signs in pulmonary tuberculosis. Accurate segmentation of pulmonary tuberculosis cavities has practical significance for indicating the activity of lesions and guiding clinical treatment. However, this task faces challenges such as blurred boundaries, irregular shapes, different location and size of lesions, and similar structures on computed tomography (CT) to other lung diseases or tissues. To overcome these problems, we propose a novel RNN-combined graph convolutional network (R2GCN) method, which integrates the bidirectional recurrent network (BRN) and graph convolution network (GCN) modules. First, feature extraction is performed on the input image by VGG-16 or ResNet-50 to obtain the feature map. The feature map is then used as the input of the two modules. On the one hand, we adopt the BRN to retrieve contextual information from the feature map. On the other hand, we take the vector for each location in the feature map as input nodes and utilize GCN to extract node topology information. Finally, two types of features obtained are fused together. Our strategy can not only make full use of node correlations and differences, but also obtain more precise segmentation boundaries. Extensive experiments on CT images of cavitary patients with tuberculosis show that our proposed method achieves best segmentation accuracy than comparison segmentation methods. Our method can be used for the diagnosis of pulmonary tuberculosis cavity and the evaluation of pulmonary tuberculosis cavity treatment.