Detecting dense landmarks for diverse clothes, as a fundamental technique for clothes analysis, has attracted increasing research attention due to its huge application potential. However, due to the lack of modeling underlying semantic layout constraints among landmarks, prior works often detect ambiguous and structure-inconsistent landmarks of multiple overlapped clothes in one person. In this paper, we propose to seamlessly enforce structural layout relationships among landmarks on the intermediate representations via multiple stacked layout-graph reasoning layers. We define the layout-graph as a hierarchical structure including a root node, body-part nodes (e.g. upper body, lower body), coarse clothes-part nodes (e.g. collar, sleeve) and leaf landmark nodes (e.g. left-collar, right-collar). Each Layout-Graph Reasoning(LGR) layer aims to map feature representations into structural graph nodes via a Map-to-Node module, performs reasoning over structural graph nodes to achieve global layout coherency via a layout-graph reasoning module, and then maps graph nodes back to enhance feature representations via a Node-to-Map module. The layout-graph reasoning module integrates a graph clustering operation to generate representations of intermediate nodes (bottom-up inference) and then a graph deconvolution operation (top-down inference) over the whole graph. Extensive experiments on two public fashion landmark datasets demonstrate the superiority of our model. Furthermore, to advance the fine-grained fashion landmark research for supporting more comprehensive clothes generation and attribute recognition, we contribute the first Fine-grained Fashion Landmark Dataset (FFLD) containing 200k images annotated with at most 32 key-points for 13 clothes types.