Human annotation of training samples is expensive, laborious, and sometimes challenging, especially for Natural Language Processing (NLP) tasks. To reduce the labeling cost and enhance the sample efficiency, Active Learning (AL) technique can be used to label as few samples as possible to reach a reasonable or similar results. To reduce even more costs and with the significant advances of Large Language Models (LLMs), LLMs can be a good candidate to annotate samples. This work investigates the accuracy and cost of using LLMs (GPT-3.5 and GPT-4) to label samples on 3 different datasets. A consistency-based strategy is proposed to select samples that are potentially incorrectly labeled so that human annotations can be used for those samples in AL settings, and we call it mixed annotation strategy. Then we test performance of AL under two different settings: (1) using human annotations only; (2) using the proposed mixed annotation strategy. The accuracy of AL models under 3 AL query strategies are reported on 3 text classification datasets, i.e., AG's News, TREC-6, and Rotten Tomatoes. On AG's News and Rotten Tomatoes, the models trained with the mixed annotation strategy achieves similar or better results compared to that with human annotations. The method reveals great potentials of LLMs as annotators in terms of accuracy and cost efficiency in active learning settings.