COVID-19 is an infectious disease with its first recorded cases identified in late 2019, while in March of 2020 it was declared as a pandemic. The outbreak of the disease has led to a sharp increase in posts and comments from social media users, with a plethora of sentiments being found therein. This paper addresses the subject of sentiment analysis, focusing on the classification of users’ sentiment from posts related to COVID-19 that originate from Twitter. The period examined is from March until mid-April of 2020, when the pandemic had thus far affected the whole world. The data is processed and linguistically analyzed with the use of several natural language processing techniques. Sentiment analysis is implemented by utilizing seven different deep learning models based on LSTM neural networks, and a comparison with traditional machine learning classifiers is made. The models are trained in order to distinguish the tweets between three classes, namely negative, neutral and positive.