The offline Siamese tracking methods have recently attracted much attention due to their impressive performance on speed and accuracy. However, they ignore the target and background information during tracking, thus lacking sufficient discrimination ability to handle complex background interference, and cannot robustly adapt to sharp appearance variations in challenging situations, such as scale variation, rotation, occlusion, and background clutter. To address the drawbacks above, we propose an online discrimination-correction subnet, which discriminates and corrects the tracking results obtained by the Siamese tracker through online learning, and further guides the template update. Firstly, a feature refinement module is designed to enhance the discriminative ability of features, which compresses and combines target features based on the importance of feature channels to obtain target-specific features. On this basis, an online discriminator module is proposed to learn the decision boundary between target and background through samples collected online to suppress background interference. In addition, a sample equilibrium strategy is proposed to alleviate the imbalance in the distribution of positive and negative samples during online training. Finally, to handle sharp target appearance variations, a robust template updating strategy is proposed to screen high-quality historical samples to generate dynamic templates. To evaluate the generalization ability and effectiveness of our method, we apply it to four classical Siamese trackers, namely SiamFC, SiamRPN++, SiamCAR, and TransT. Extensive experiments on seven challenging benchmarks demonstrate that our method significantly improves the baseline methods and achieves outstanding performance compared with state-of-the-art trackers.