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Background: Most first-year college/university students are adolescents or young adults and therefore are at high risk of developing psychological distress symptoms. Little is known about psychological distress among first-year university students in Taiwan, especially those studying health science-related fields. Objective: To understand the prevalence of psychological distress and its five dimensions (depression and anxiety, self-harm, impulsivity, and psychiatric disturbance) and explore the relationship between student-specific variables (enrollment year, age, sex, program duration, and college) and psychological distress. Methods: A secondary analysis design was adopted. We enrolled 4,212 first-year university students throughout 2016, 2017, and 2018. Health screening data were obtained using the Mental Health Scale for Undergraduate-Screening Assessment (MHSU-SA) for first-year health science students at a private technical-vocational university in northern Taiwan. Results: Many first-year university students were at-risk for depression (4.2%), anxiety (8.2%), self-harm (5.2%), impulsivity (2.6%), psychiatric disturbance (4.4%), and overall psychological distress (4.2%). Students in a four-year program were more than twice as likely to demonstrate psychological distress symptoms compared to their two-year (night) program counterparts (odds ratio = 2.05, 95% confidence interval = 1.20–3.49, p < 0.01). Conclusion: Some first-year health science university students showed psychological distress, including anxiety, self-harm, psychiatric disturbance, depression, and impulsivity. Students in four-year programs were twice as likely to show symptoms of psychological distress than those in two-year (night) programs. Therefore, mental health screenings are recommended to facilitate early detection and timely intervention for at-risk students.