The World Health Organization (WHO) declared the COVID-19 outbreak has resulted in more than six million confirmed cases and more than 371,000 deaths globally on June 1, 2020. The incident sparked a flood of scientific research to help society deal with the virus, both inside and outside the medical domain. Research related to public health analysis and public conversations about the spread of COVID-19 on social media is one of the highlights of researchers in the world. People can analyze information from social media as supporting data about public health. Analyzing public conversations will help the relevant authorities understand public opinion and information gaps between them and the public, helping them develop appropriate emergency response strategies to address existing problems in the community during the pandemic and provide information on the population's emotions in different contexts. However, research related to the analysis of public health and public conversations was so far conducted only through supervised analysis of textual data. In this study, we aim to analyze specifically the sentiment and topic modeling of Indonesian public conversations about the COVID-19 on Twitter using the NLP technique. We applied some methods to analyze the sentiment to obtain the best classification method. In this study, the topic modeling was carried out unsupervised using Latent Dirichlet Allocation (LDA). The results of this study reveal that the most frequently discussed topic related to the COVID-19 pandemic is economic issues.