Effective real-world multi-agent collaboration requires not only accurate planning but also the ability to reason about collaborators' intents--a crucial capability for avoiding miscoordination and redundant communication under partial observable environments. Due to their strong planning and reasoning capabilities, large language models (LLMs) have emerged as promising autonomous agents for collaborative task solving. However, existing collaboration frameworks for LLMs overlook their reasoning potential for dynamic intent inference, and thus produce inconsistent plans and redundant communication, reducing collaboration efficiency. To bridge this gap, we propose CoBel-World, a novel framework that equips LLM agents with a Collaborative Belief World--an internal representation jointly modeling the physical environment and collaborators' mental states. CoBel-World enables agents to parse external open-world knowledge into structured beliefs via a symbolic belief representation module, and perform zero-shot Bayesian-style belief updates through LLM reasoning. This allows agents to proactively detect potential miscoordination (e.g., conflicting plans) and communicate adaptively. Evaluated on challenging embodied benchmarks (i.e., TDW-MAT and C-WAH), CoBel-World significantly reduces communication costs by 64-79% and improves task completion efficiency by 4-28% compared to the strongest baseline. Our results show that explicit, intent-aware belief modeling is essential for efficient and human-like collaboration in LLM-based multi-agent systems.