Scene Graph Generation (SGG) aims to explore the relationships between objects in images and obtain scene summary graphs, thereby better serving downstream tasks. However, the long-tailed problem has adversely affected the scene graph's quality. The predictions are dominated by coarse-grained relationships, lacking more informative fine-grained ones. The union region of one object pair (i.e., one sample) contains rich and dedicated contextual information, enabling the prediction of the sample-specific bias for refining the original relationship prediction. Therefore, we propose a novel Sample-Level Bias Prediction (SBP) method for fine-grained SGG (SBG). Firstly, we train a classic SGG model and construct a correction bias set by calculating the margin between the ground truth label and the predicted label with the trained classic SGG model. Then, we devise a Bias-Oriented Generative Adversarial Network (BGAN) that learns to predict the constructed correction biases, which can be utilized to correct the original predictions from coarse-grained relationships to fine-grained ones. The extensive experiments on VG and GQA datasets demonstrate that our SBG outperforms the state-of-the-art methods in terms of Average@K across three mainstream SGG models: Motif, VCtree, and Transformer. Compared to dataset-level correction methods, our SBG shows a significant average improvement of 5.6%, 3.9%, and 3.2% on Average@K for tasks PredCls, SGCls, and SGDet, respectively. The code will be available publicly.