Volumetric design is the first and critical step for professional building design, where architects not only depict the rough 3D geometry of the building, but also specify the programs to form a 2D layout on each floor. Though 2D layout generation for a single story has been widely studied, there is no developed method for multi-story buildings. This paper focuses on volumetric design generation conditioned on an input program graph. Instead of outputting dense 3D voxels, we propose a new 3D representation named voxel graph that is both compact and expressive for building geometries. Our generator is a cross-modal graph neural network that uses a pointer mechanism to connect the input program graph and the output voxel graph, and the whole pipeline is trained using the adversarial framework. The generated designs are evaluated qualitatively by a user study and quantitatively using three metrics–quality, diversity, and connectivity accuracy. We show that our model generates realistic 3D volumetric designs and outperforms previous methods and baselines.