The aim was to identify maternal and paternal socioeconomic and demographic characteristics for non-initiation and non-completion of the human papillomavirus (HPV) vaccination among Danish girls including time-trends. This nationwide register-based cohort study included all girls residing in Denmark who were offered free-of-charge HPV vaccination as a part of the childhood vaccination program between 2009 and 2018 (birth cohorts 1996-2005). The study samples included 296,461 daughter-mother dyads and 291,025 daughter-father dyads. Data from the Danish Vaccination Register were linked with socioeconomic and demographic data from Statistics Denmark. HPV vaccination status was classified as 'non-initiation' for girls who received no HPV vaccine and as 'non-completion' for girls who initiated the HPV vaccination program but did not receive all the scheduled HPV vaccines. Data were analyzed using logistic regression models. Non-initiation of HPV vaccination was 13.7%, and non-completion was 24.2% among girls who initiated the HPV vaccination program. Girls of parents who were descendants of immigrants (adjusted odds ratio: 1.50; 95% confidence interval: 1.35-1.68), were at least 35-years old at time of birth, had basic or no education, had a low income, were not in the labor market, and were unmarried had the highest non-initiation and non-completion odds. The associations between socioeconomic and demographic characteristics and HPV vaccination uptake were similar for mothers and fathers. Despite free-of-charge availability to HPV vaccination in Denmark, we found disparities in non-initiation and non-completion of HPV vaccination among Danish girls by both mothers' and fathers' socioeconomic and demographic characteristics.