Object trajectory prediction is a hot research issue with wide applications in video surveillance and autonomous driving. The previous studies consider the interaction sparsity mainly among the pedestrians instead of multi-type of objects, which brings new types of interactions and consequently superfluous ones. This paper proposes a Multi-type Object Trajectory Prediction (MOTP) method with a Sparse Multi-relational Graph Convolutional Network (SMGCN) and a novel multi-round Global Temporal Aggregation (GTA). MOTP introduces a novel adaptive sparsification and multi-scale division method to model interactions among multitype of objects. It further incorporates a Sparse Multi-relational Temporal Graph to capture the temporal division of multi-type trajectories, along with a multi-round Global Temporal Aggregation (GTA) mechanism to mitigate error accumulation, and enhances the trajectory prediction accuracy. The extensive evaluation on the ETH, UCY and SDD datasets shows that our method outperforms the typical state-of-the-art works by significant margins. Codes will be available in https://github.com/ sounio/SMGCN.