Robot manipulation policies have shown unsatisfactory action performance when confronted with novel task or object instances. Hence, the capability to automatically detect and self-correct failure action is essential for a practical robotic system. Recently, Multimodal Large Language Models (MLLMs) have shown promise in visual instruction following and demonstrated strong reasoning abilities in various tasks. To unleash general MLLMs as an end-to-end robotic agent, we introduce a Self-Corrected (SC)-MLLM, equipping our model not only to predict end-effector poses but also to autonomously recognize and correct failure actions. Specifically, we first conduct parameter-efficient fine-tuning to empower MLLM with pose prediction ability, which is reframed as a language modeling problem. When facing execution failures, our model learns to identify low-level action error causes (i.e., position and rotation errors) and adaptively seeks prompt feedback from experts. Based on the feedback, SC-MLLM rethinks the current failure scene and generates the corrected actions. Furthermore, we design a continuous policy learning method for successfully corrected samples, enhancing the model's adaptability to the current scene configuration and reducing the frequency of expert intervention. To evaluate our SC-MLLM, we conduct extensive experiments in both simulation and real-world settings. SC-MLLM agent significantly improve manipulation accuracy compared to previous state-of-the-art robotic MLLM (ManipLLM), increasing from 57\% to 79\% on seen object categories and from 47\% to 69\% on unseen novel categories.