Widespread population vaccination against the SARS-CoV-2 virus is a matter of great interest to public health as it is the main pharmacological measure to contain the COVID-19 pandemic. Hesitancy/reluctance to vaccination has become a main barrier to containing the pandemic. Young adults are the age group with the greatest resistance to vaccination, even in countries with the highest vaccination rates during this pandemic. The objective of this study was to identify the main predictive factors of vaccination intention and profile people with hesitancy/reluctance to vaccinate against SARS-CoV-2 virus in young adults living in Spain during the pandemic. A cross-sectional study was conducted based on the administration of an online survey (PSY-COVID-2) that evaluated the intention of vaccination together with a wide range of sociodemographic, social, cognitive, behavioral and affective variables in a sample of 2210 young adults. 14% of the sample showed hesitancy/reluctance to vaccination at the beginning of their vaccination campaign. A total of 35 factors were associated (small to medium effect sizes) with the intention to get vaccinated. A reduced set of 4 attitudinal and social variables explained 41% of the variability in vaccination intention: attitude to the vaccination, trust in health staff/scientists, conspiracy beliefs about SARS-CoV-2 and time spent being informed about COVID-19. These variables showed good sensitivity/specificity for classifying people as reluctant/not reluctant to vaccination, properly classifying 86% of people. Psychosocial processes related to attitudes, trust and information are the main predictors of vaccination intention in a highly reluctant group such as the young adult population.