We propose Neural Turtle Graphics (NTG), a novel gen- erative model for spatial graphs, and demonstrate its ap- plications in modeling city road layouts. Specifically, we represent the city road layout using a graph where nodes in the graph represent control points and edges in the graph represents segment of roads. NTG is a sequential genera- tive model parameterized by a neural network. It iteratively generates a new node and an edge connecting to an existing node conditioned on the current graph. We train the NTG model on Open Street Map data and show it outperforms ex- isting generative models using a set of diverse performance metrics. Moreover, our method allows users to control styles of generated road layouts mimicking existing cities as well as to sketch a part of the city road layout to be synthesized. In addition to synthesis, the proposed NTG finds uses in an analytical task of aerial road parsing. Experimental results show that it achieves state-of-the-art performance on the SpaceNet dataset.