High-level synthesis (HLS) is widely used for transferring behavior-level specifications into circuit-level implementations. As a critical step in HLS, scheduling arranges the execution order of operations for enhanced performance. However, existing scheduling methods suffer from either exponential runtime or poor quality of solutions. This paper proposes an efficient and effective GNN-based scheduling method called NeuroSchedule, with both fast runtime and enhanced solution quality. Major features are as follows: (1) The learning problem for HLS scheduling is formulated for the first time, and a new machine learning framework is proposed. (2) Pre-training models are adopted to further enhance the scalability for various scheduling problems with different settings. Experimental results show that NeuroSchedule obtains near-optimal solutions while achieving more than 50,000x improvement in runtime compared with the ILP-based scheduling method. At the same time, NeuroSchedule improves the scheduling results by 6.10% on average compared with state-of-the-art entropy-directed method. To the best of our knowledge, this is the first GNN-based scheduling method for HLS.