The COVID-19 pandemic has resulted in a surge of fake news, creating public health risks. However, developing an effective way to detect such news is challenging, especially when published news involves mixing true and false information. Detecting COVID-19 fake news has become a critical task in the field of natural language processing (NLP). This paper explores the effectiveness of several machine learning algorithms and fine-tuning pre-trained transformer-based models, including Bidirectional Encoder Representations from Transformers (BERT) and COVID-Twitter-BERT (CT-BERT), for COVID-19 fake news detection. We evaluate the performance of different downstream neural network structures, such as CNN and BiGRU layers, added on top of BERT and CT-BERT with frozen or unfrozen parameters. Our experiments on a real-world COVID-19 fake news dataset demonstrate that incorporating BiGRU on top of the CT-BERT model achieves outstanding performance, with a state-of-the-art F1 score of 98%. These results have significant implications for mitigating the spread of COVID-19 misinformation and highlight the potential of advanced machine learning models for fake news detection.