Learning policies from offline datasets through offline reinforcement learning (RL) holds promise for scaling data-driven decision-making and avoiding unsafe and costly online interactions. However, real-world data collected from sensors or humans often contains noise and errors, posing a significant challenge for existing offline RL methods. Our study indicates that traditional offline RL methods based on temporal difference learning tend to underperform Decision Transformer (DT) under data corruption, especially when the amount of data is limited. This suggests the potential of sequential modeling for tackling data corruption in offline RL. To further unleash the potential of sequence modeling methods, we propose Robust Decision Transformer (RDT) by incorporating several robust techniques. Specifically, we introduce Gaussian weighted learning and iterative data correction to reduce the effect of corrupted data. Additionally, we leverage embedding dropout to enhance the model's resistance to erroneous inputs. Extensive experiments on MoJoCo, KitChen, and Adroit tasks demonstrate RDT's superior performance under diverse data corruption compared to previous methods. Moreover, RDT exhibits remarkable robustness in a challenging setting that combines training-time data corruption with testing-time observation perturbations. These results highlight the potential of robust sequence modeling for learning from noisy or corrupted offline datasets, thereby promoting the reliable application of offline RL in real-world tasks.