Developing autonomous agents capable of mastering complex, multi-step tasks in unpredictable, interactive environments presents a significant challenge. While Large Language Models (LLMs) offer promise for planning, existing approaches often rely on problematic internal knowledge or make unrealistic environmental assumptions. Although recent work explores learning planning knowledge, they still retain limitations due to partial reliance on external knowledge or impractical setups. Indeed, prior research has largely overlooked developing agents capable of acquiring planning knowledge from scratch, directly in realistic settings. While realizing this capability is necessary, it presents significant challenges, primarily achieving robustness given the substantial risk of incorporating LLMs' inaccurate knowledge. Moreover, efficiency is crucial for practicality as learning can demand prohibitive exploration. In response, we introduce Robust and Efficient Planning for Open-world Agents (REPOA), a novel framework designed to tackle these issues. REPOA features three key components: adaptive dependency learning and fine-grained failure-aware operation memory to enhance robustness to knowledge inaccuracies, and difficulty-based exploration to improve learning efficiency. Our evaluation in two established open-world testbeds demonstrates REPOA's robust and efficient planning, showcasing its capability to successfully obtain challenging late-game items that were beyond the reach of prior approaches.