This work introduces a framework harnessing the capabilities of Large Language Models (LLMs) to generate primitive task conditions for generalizable long-horizon manipulations with novel objects and unseen tasks. These task conditions serve as guides for the generation and adjustment of Dynamic Movement Primitives (DMP) trajectories for long-horizon task execution. We further create a challenging robotic manipulation task suite based on Pybullet for long-horizon task evaluation. Extensive experiments in both simulated and real-world environments demonstrate the effectiveness of our framework on both familiar tasks involving new objects and novel but related tasks, highlighting the potential of LLMs in enhancing robotic system versatility and adaptability. Project website: https://object814.github.io/Task-Condition-With-LLM/