Climate change has been a worldwide concern for more than 50 years, and climate change misinformation has also become a critical issue as it questions the causes and effects of climate change, thereby disrupting climate action. Climate misinformation has been a major obstacle to mitigating climate change and its effects, aggravating the issue and polarizing the public. In this paper, we introduce ClimateMiSt, a new climate change misinformation and stance detection dataset consisting of social media data with manually verified labels. The data is collected from Twitter/X and our dataset contains 146,670 tweets. We implement state-of-the-art baseline models for both misinformation and stance detection on our dataset and discover that GPT-4 outperforms them in both tasks. To the best of our knowledge, ClimateMiSt is the first dataset focused on climate change that includes both veracity and stance annotations collected from a social media platform. Our novel dataset can be used for climate change misinformation and stance detection, and it can further contribute to research in this field.