Autonomous agents powered by large language models (LLMs) have shown impressive capabilities in tool manipulation for complex task-solving. However, existing paradigms such as ReAct rely on sequential reasoning and execution, failing to exploit the inherent parallelism among independent sub-tasks. This sequential bottleneck leads to inefficient tool utilization and suboptimal performance in multi-step reasoning scenarios. We introduce Graph-based Agent Planning (GAP), a novel framework that explicitly models inter-task dependencies through graph-based planning to enable adaptive parallel and serial tool execution. Our approach trains agent foundation models to decompose complex tasks into dependency-aware sub-task graphs, autonomously determining which tools can be executed in parallel and which must follow sequential dependencies. This dependency-aware orchestration achieves substantial improvements in both execution efficiency and task accuracy. To train GAP, we construct a high-quality dataset of graph-based planning traces derived from the Multi-Hop Question Answering (MHQA) benchmark. We employ a two-stage training strategy: supervised fine-tuning (SFT) on the curated dataset, followed by reinforcement learning (RL) with a correctness-based reward function on strategically sampled queries where tool-based reasoning provides maximum value. Experimental results on MHQA datasets demonstrate that GAP significantly outperforms traditional ReAct baselines, particularly on multi-step retrieval tasks, while achieving dramatic improvements in tool invocation efficiency through intelligent parallelization. The project page is available at: https://github.com/WJQ7777/Graph-Agent-Planning.