Machine learning-based classifiers have been used for text classification, such as sentiment analysis, news classification, and toxic comment classification. However, supervised machine learning models often require large amounts of labeled data for training, and manual annotation is both labor-intensive and requires domain-specific knowledge, leading to relatively high annotation costs. To address this issue, we propose an approach that integrates large language models (LLMs) into an active learning framework, achieving high cross-task text classification performance without the need for any manually labeled data. Furthermore, compared to directly applying GPT for classification tasks, our approach retains over 93% of its classification performance while requiring only approximately 6% of the computational time and monetary cost, effectively balancing performance and resource efficiency. These findings provide new insights into the efficient utilization of LLMs and active learning algorithms in text classification tasks, paving the way for their broader application.