We propose LEO-RobotAgent, a general-purpose language-driven intelligent agent framework for robots. Under this framework, LLMs can operate different types of robots to complete unpredictable complex tasks across various scenarios. This framework features strong generalization, robustness, and efficiency. The application-level system built around it can fully enhance bidirectional human-robot intent understanding and lower the threshold for human-robot interaction. Regarding robot task planning, the vast majority of existing studies focus on the application of large models in single-task scenarios and for single robot types. These algorithms often have complex structures and lack generalizability. Thus, the proposed LEO-RobotAgent framework is designed with a streamlined structure as much as possible, enabling large models to independently think, plan, and act within this clear framework. We provide a modular and easily registrable toolset, allowing large models to flexibly call various tools to meet different requirements. Meanwhile, the framework incorporates a human-robot interaction mechanism, enabling the algorithm to collaborate with humans like a partner. Experiments have verified that this framework can be easily adapted to mainstream robot platforms including unmanned aerial vehicles (UAVs), robotic arms, and wheeled robot, and efficiently execute a variety of carefully designed tasks with different complexity levels. Our code is available at https://github.com/LegendLeoChen/LEO-RobotAgent.