Large Language Models (LLMs) have brought significant advances across various NLP tasks through few-shot or zero-shot prompting, bypassing the need for parameter tuning. However, the "black-box" nature behind their massive parameter sizes increases the "hallucination" concerns, especially in high-stakes applications (e.g., healthcare), where decision mistakes can lead to severe consequences. In contrast, human decision-making relies on complex cognitive processes, such as the ability to sense and adaptively correct mistakes through conceptual understanding. Drawing inspiration from human cognition, we propose an innovative metacognitive approach CLEAR, to equip LLMs with capabilities for self-aware error identification and correction. Our framework constructs concept-specific sparse subnetworks that indicate decision processes. This provides a novel interface for model {intervention} after deployment. The benefits include: (i) at inference time, our metacognitive LLMs can self-consciously identify potential mispredictions with minimum human involvement, (ii) the model can self-correct its errors efficiently without additional tuning, and (iii) the correction procedure is not only self-explanatory but also user-friendly, enhancing model interpretability and accessibility. With these metacognitive features, our approach pioneers a new path toward the trustworthiness of LLMs.