Since the first alert launched by the World Health Organization (5 January, 2020), COVID-19 has been spreading out to almost 200 countries and territories. As of January 23, 2022, in total, over 346 million confirmed cases and over 5.5 million deaths have been reported worldwide. This causes massive losses in the economy and jobs globally and confining about 58% of the global population. In this paper, we introduce SenWave, a novel sentimental analysis work using 106+ million collected tweets and Weibo messages to evaluate the global rise and falls of sentiments during the COVID-19 pandemic. To make a fine-grained analysis on the feeling when we face this global health crisis, we annotate 10K tweets in English and 10K tweets in Arabic in 10 categories, including optimistic, thankful, empathetic, pessimistic, anxious, sad, annoyed, denial, official report, and joking. We then utilize an integrated transformer framework, called simpletransformer, to conduct multi-label sentimental classification by fine-tuning the pre-trained language model on the labeled data. Meanwhile, in order for a more complete analysis, we also translate the annotated English tweets into different languages (Spanish, Italian, and French) to generated training data for building sentiment analysis models for these languages. We provide detailed analysis and interesting discoveries on how the emotions evolve overtime. SenWave thus reveals the sentiment of global conversation in six different languages on COVID-19 (covering English, Spanish, French, Italian, Arabic and Chinese), followed the spread of the epidemic. The conversation showed a remarkably similar pattern of rapid rise and slow decline over time across all nations, as well as on special topics like the herd immunity strategies, to which the global conversation reacts strongly negatively. Overall, SenWave shows that optimistic and positive sentiments increased over time, foretelling a desire to seek, together, a reset for an improved COVID-19 world. We share the dataset with public to help other social impact studies of Covid-19, and fine-grained sentimental analysis tasks.