In multi-task learning (MTL), we improve the performance of key machine learning algorithms by training various tasks jointly. When the number of tasks is large, modeling task structure can further refine the task relationship model. For example, often tasks can be grouped based on metadata, or via simple preprocessing steps like K-means. In this paper, we present our group structured latent-space multi-task learning model, which encourages group structured tasks defined by prior information. We use an alternating minimization method to learn the model parameters. Experiments are conducted on both synthetic and real-world datasets, showing competitive performance over single-task learning (where each group is trained separately) and other MTL baselines.