By taking the semantic object parsing task as an exemplar application scenario, we propose the Graph Long Short-Term Memory (Graph LSTM) network, which is the generalization of LSTM from sequential data or multidimensional data to general graph-structured data. Particularly, instead of evenly and fixedly dividing an image to pixels or patches in existing multi-dimensional LSTM structures (e.g., Row, Grid and Diagonal LSTMs [1][2]), we take each arbitrary-shaped superpixel as a semantically consistent node, and adaptively construct an undirected graph for each image, where the spatial relations of the superpixels are naturally used as edges. Constructed on such an adaptive graph topology, the Graph LSTM is more naturally aligned with the visual patterns in the image (e.g., object boundaries or appearance similarities) and provides a more economical information propagation route. Furthermore, for each optimization step over Graph LSTM, we propose to use a confidence-driven scheme to update the hidden and memory states of nodes progressively till all nodes are updated. In addition, for each node, the forgets gates are adaptively learned to capture different degrees of semantic correlation with neighboring nodes. Comprehensive evaluations on four diverse semantic object parsing datasets well demonstrate the significant superiority of our Graph LSTM over other state-of-the-art solutions.