Background: Insomnia is the most recognized sleep disorder. The time of the COVID-19 pandemic brings with it new challenges. During the COVID-19 pandemic, maintaining sleep hygiene is highly recommended as it helps to strengthen the immune system, and people infected with COVID-19 may be more prone to sleep problems.The aim of this study was to determine the incidence of insomnia among people aged 18-25 during the COVID-19 pandemic. Methods: The study involved 302 individuals. It was conducted using Google Forms. The mean age of the respondents was 23 ± 1.84 years. The research instruments used in the study were the Athenian Insomnia Scale (AIS), the Beck Depression Inventory (BDI), and the author’s questionnaire concerning sociodemographic data. Results: Insomnia was found in 29.5% (n = 89) of the respondents. Higher mean values (8 ± 4.19) in the AIS were noted in the group of people with higher education and those currently studying. Moderate depression was demonstrated in 12.6% (n = 38) of the subjects. One third (30.1%; n = 91) of the respondents indicated greater sleep problems during the COVID-19 pandemic than before. Conclusions: Insomnia and depression are significant problems in the study group of 18-25 year olds. Therefore, psychological and psychiatric care should be extended to this group of young people.