COVID-19 vaccinations are essential to mitigate the pandemic and prevent severe SARS-CoV-2 infections. However, the serum antibody levels in vaccinated individuals gradually decrease over time, while SARS-CoV-2 is undergoing an evolution toward more transmissible variants, such as B.1.617.2, ultimately increasing the risk of breakthrough infections and further virus spread. This cross-sectional online study of adult Poles (n = 2427) was conducted in September 2021 (before a general recommendation to administer a booster COVID-19 vaccine dose in Poland was issued) to assess the attitude of individuals who completed the current vaccination regime toward a potential booster dose of the COVID-19 vaccine and identify potential factors that may influence it. Overall, 71% of participants declared willingness to receive a booster COVID-19 dose, with a low median level of fear of receiving it of 1.0 (measured by the 10-point Likert-type scale), which was increased particularly in those having a worse experience (in terms of severity of side effects and associated fear) with past COVID-19 vaccination. The lowest frequency of willingness to receive a booster dose (26.7%) was seen in the group previously vaccinated with Ad26.COV2.S. The majority of individuals vaccinated previously with mRNA vaccines wished to receive the same vaccine, while in the case of AZD1222, such accordance was observed only in 9.1%. The main reasons against accepting a booster COVID-19 dose included the side effects experienced after previous doses, the opinion that further vaccination is unnecessary, and safety uncertainties. Women, older individuals (≥50 years), subjects with obesity, chronic diseases, and pre-vaccination and post-vaccination SARS-CoV-2 infections, and those with a history of vaccination against influenza were significantly more frequently willing to receive a booster COVID-19 dose. Moreover, the majority of immunosuppressed individuals (88%) were willing to receive an additional dose. The results emphasize some hesitancy toward potential further COVID-19 vaccination in the studied group of Poles and indicate the main groups to be targeted with effective science communication regarding the booster doses.