This study aimed to find the prevalence of stress, anxiety, depression, and PTSD; differences according to demographic variables; and predictors of mental health problems during the second wave of the coronavirus disease (COVID-19) pandemic in Turkey. Differences in exposure to COVID-19 during the first and second waves of the pandemic among students were compared. A total of 754 students from seven universities in different parts of Turkey participated in the survey between November and December 2020. Perceived Stress Scale (PSS-10), Generalized Anxiety Disorder (GAD-7), Patient Health Questionnaire (PHQ-9), Checklist-Civilian Version (PCL-C) scale measuring posttraumatic stress disorder (PTSD), and Satisfaction with Life Scale (SWLS) were used to measure the mental well-being of students. Descriptive statistics, one-way ANOVA, correlations, and multinomial logistic regression methods were used to analyze the data. The prevalence of high stress, high generalized anxiety (GAD-7 ≥ 10), high depression symptoms (PHQ-9 ≥ 10), and high PTSD in the total sample were 84.2, 36.2, 55.0, and 61.2%, respectively. High perceived stress, moderate generalized anxiety disorder, mild depression symptoms, high severity PTSD, and moderate satisfaction were found among students in Turkey. Religiosity and spirituality have significant negative correlations with anxiety, depression, and PTSD. Religiosity level, gender, relationship status, year of study, physical activity, symptoms of coronavirus, death of a close relative, job loss, and economic status are significant parameters for predicting psychological problems of students in Turkey.