The rapid evolution of Large Language Models (LLMs) has enabled the industry to develop various AI-based services. Instruction tuning is considered essential in adapting foundation models for target domains to provide high-quality services to customers. A key challenge in instruction tuning is obtaining high-quality instruction data. Self-Instruct, which automatically generates instruction data using ChatGPT APIs, alleviates the data scarcity problem. To improve the quality of instruction data, Self-Instruct discards many of the instructions generated from ChatGPT, even though it is inefficient in terms of cost owing to many useless API calls. To generate high-quality instruction data at a low cost, we propose a novel data generation framework, Self-Direct Instruction generation (SeDi-Instruct), which employs diversity-based filtering and iterative feedback task generation. Diversity-based filtering maintains model accuracy without excessively discarding low-quality generated instructions by enhancing the diversity of instructions in a batch. This reduces the cost of synthesizing instruction data. The iterative feedback task generation integrates instruction generation and training tasks and utilizes information obtained during the training to create high-quality instruction sets. Our results show that SeDi-Instruct enhances the accuracy of AI models by 5.2%, compared with traditional methods, while reducing data generation costs by 36%.