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Current methods using Large Language Models (LLMs) suffer from a fundamental trade-off: generating linear sequences is efficient but fails to model parallelism and adapt to changes, while iterative querying is adaptive but too slow and costly. To bridge this gap, we introduce DAG-Plan, a novel task planning framework that for the first time employs a Directed Acyclic Graph (DAG) as the central representation for dual-arm coordination. The key insight is that a DAG natively captures complex sub-task dependencies and explicitly reveals opportunities for parallel execution. Within this framework, an LLM is used only once as a powerful semantic parser to translate a natural language instruction into a structured DAG. 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