Traffic flow forecasting plays a vital role in the transportation domain. Existing studies usually manually construct correlation graphs and design sophisticated models for learning spatial and temporal features to predict future traffic states. However, manually constructed correlation graphs cannot accurately extract the complex patterns hidden in the traffic data. In addition, it is challenging for the prediction model to fit traffic data due to its irregularly-shaped distribution. To solve the above-mentioned problems, in this paper, we propose a novel learning-based method to learn a spatial-temporal correlation graph, which could make good use of the traffic flow data. Moreover, we propose First-Order Gradient Supervision (FOGS), a novel method for traffic flow forecasting. FOGS utilizes first-order gradients, rather than specific flows, to train prediction model, which effectively avoids the problem of fitting irregularly-shaped distributions. Comprehensive numerical evaluations on four real-world datasets reveal that the proposed methods achieve state-of-the-art performance and significantly outperform the benchmarks.