Layout is important for graphic design and scene generation. We propose a novel Generative Adversarial Network, called LayoutGAN, that synthesizes layouts by modeling geometric relations of different types of 2D elements. The generator of LayoutGAN takes as input a set of randomly-placed 2D graphic elements, represented by vectors and uses self-attention modules to refine their labels and geometric parameters jointly to produce a realistic layout. Accurate alignment is critical for good layouts. We, thus, propose a novel differentiable wireframe rendering layer that maps the generated layout to a wireframe image, upon which a CNN-based discriminator is used to optimize the layouts in image space. We validate the effectiveness of LayoutGAN in various experiments including MNIST digit generation, document layout generation, clipart abstract scene generation, tangram graphic design, mobile app layout design, and webpage layout optimization from hand-drawn sketches.