In recent years, excessive emissions of carbon dioxide have further intensified global warming, which poses a great threat to human society. The best way to reverse this situation is to take action to equalize the "carbon emissions" with the "carbon absorption," i.e., carbon neutrality (CN). To better understand the evolution and display a broad panorama of CN research, this paper provides a comprehensive bibliometric analysis of publications in the field of CN from 2006 to 2021. We use the Web of Science Core Collection as the data source, and a total of 633 publications have been retrieved. In the paper, we measure the productivity and influence of publications through recognized bibliometric metrics, and visually analyze publications using VOS Viewer and CiteSpace. The analysis results show that China is the most productive country/region. The study illustrates that in order to reach the goal of CN, it is necessary to reduce carbon emissions such as full using renewable energy. Simultaneously, it is also essential to enhance the "negative emissions" of carbon such as taking advantage of carbon sink and carbon capture, utilization, and storage. This paper provides some references for scholars who are interested or research in this field.