Dual-arm robots offer enhanced versatility and efficiency over single-arm counterparts by enabling concurrent manipulation of multiple objects or cooperative execution of tasks using both arms. However, effectively coordinating the two arms for complex long-horizon tasks remains a significant challenge. Existing task planning methods predominantly focus on single-arm robots or rely on predefined bimanual operations, failing to fully leverage the capabilities of dual-arm systems. To address this limitation, we introduce DAG-Plan, a structured task planning framework tailored for dual-arm robots. DAG-Plan harnesses large language models (LLMs) to decompose intricate tasks into actionable sub-tasks represented as nodes within a directed acyclic graph (DAG). Critically, DAG-Plan dynamically assigns these sub-tasks to the appropriate arm based on real-time environmental observations, enabling parallel and adaptive execution. We evaluate DAG-Plan on the novel Dual-Arm Kitchen Benchmark, comprising 9 sequential tasks with 78 sub-tasks and 26 objects. Extensive experiments demonstrate the superiority of DAG-Plan over directly using LLM to generate plans, achieving nearly 50% higher efficiency compared to the single-arm task planning baseline and nearly double the success rate of the dual-arm task planning baseline.