Large language models (LLMs) have been demonstrated to possess the capabilities to understand fundamental graph properties and address various graph reasoning tasks. Existing methods fine-tune LLMs to understand and execute graph reasoning tasks by specially designed task instructions. However, these Text-Instruction methods generally exhibit poor performance. Inspired by tool learning, researchers propose Tool-Instruction methods to solve various graph problems by special tool calling (e.g., function, API and model), achieving significant improvements in graph reasoning tasks. Nevertheless, current Tool-Instruction approaches focus on the tool information and ignore the graph structure information, which leads to significantly inferior performance on small-scale LLMs (less than 13B). To tackle this issue, we propose GraphTool-Instruction, an innovative Instruction-tuning approach that decomposes the graph reasoning task into three distinct subtasks (i.e., graph extraction, tool name identification and tool parameter extraction), and design specialized instructions for each subtask. Our GraphTool-Instruction can be used as a plug-and-play prompt for different LLMs without fine-tuning. Moreover, building on GraphTool-Instruction, we develop GTools, a dataset that includes twenty graph reasoning tasks, and create a graph reasoning LLM called GraphForge based on Llama3-8B. We conduct extensive experiments on twenty graph reasoning tasks with different graph types (e.g., graph size or graph direction), and we find that GraphTool-Instruction achieves SOTA compared to Text-Instruction and Tool-Instruction methods. Fine-tuned on GTools, GraphForge gets further improvement of over 30% compared to the Tool-Instruction enhanced GPT-3.5-turbo, and it performs comparably to the high-cost GPT-4o. Our codes and data are available at https://anonymous.4open.science/r/GraphTool-Instruction.