Structured grid layouts are preferable in many 2D visual content creation scenarios since their structures facilitate further layout editing. Multiple geometry-based methods can effectively create structured grid layouts but require user-provided constraints or rules. Existing data-driven approaches have achieved remarkable layout generation performance, but fail to produce appropriate layout structures. We present GTLayout, a novel generative model for structured grid layout generation. We adopt general trees to represent structured grid layouts and exploit a recursive neural network (RvNN) for this generation task. Our model can handle grid layouts with varied structures and regular arrangements. Qualitative and quantitative experiments on public grid layout datasets show that our method outperforms several baselines in the tasks of layout reconstruction and layout generation, especially for datasets containing few samples. We also demonstrate that the structured layout space constructed by our method can blend structures of layouts, as well as providing a visualization and analysis of the layout space. Additionally, we consider two application cases based on GTLayout: multiple layout interpolation and conditional layout generation. Our code is available at https://github.com/Warren-swr/GT-Layout.