(1) Background: COVID-19 vaccination hesitancy is a threat for fragile patients. We aimed to evaluate COVID-19 vaccination hesitancy and its reasons in a population of liver transplant (LT) recipients. (2) Methods: In February 2021, a questionnaire on COVID-19 vaccines was sent to LT patients followed at our liver transplant outpatient clinic in Milan, Italy. Sociodemographic and clinical characteristics were recorded. Patients were defined as willing, hesitant, or refusing and their reasons were investigated. Associations between baseline characteristics and willingness were evaluated. Since March 2021, when the COVID-19 vaccines became available for LT candidates and recipients in Italy, the entire cohort of LT recipients was contacted by phone and called for vaccination, and the rate of refusals recorded. (3) Results: The web-based survey was sent to 583 patients, of whom 190 responded (response rate of 32.6%). Among the respondents to the specific question about hesitancy (184), 157 (85.3%) were willing to be vaccinated against COVID-19, while 27 (14.7%) were hesitant. Among the hesitant, three were totally refusing, for a refusal rate of 1.6%. Thirteen hesitant patients (48.1%) answered that their COVID-19 vaccination hesitancy was influenced by being a transplant recipient. The fear of adverse effects was the main reason for refusal (81.5%). Of the 711 LT patients followed at our center, 668 got fully vaccinated, while 43 (6.1%) of them refused the scheduled vaccination. (4) Conclusions: Most patients accepted COVID-19 vaccines, although 6.1% refused the vaccine. Since it is crucial to achieve adequate vaccination of LT patients, it is very important to identify the reasons influencing COVID-19 vaccination hesitancy so that appropriate and targeted communication strategies can be established and specific vaccination campaigns further implemented.