Sport anxiety not only impacts the performance of college athletes but also influences their psychological well-being. The psychological well-being of sports students is crucial for both academic performance and competition, as they need to balance their academic performance with professional athletic training. Based on self-determination theory, this study examines the relationship between various factors in sport anxiety (somatic anxiety, worry, and concentration disruption) and subjective happiness, as well as the mediating role of need satisfaction in this relationship. A total of 835 college athletic students participated in the study, completing the Sport Anxiety Scale-2, Basic Psychological Needs Satisfaction Scale-in General, and Subjective Happiness Scale. An analysis of gender differences revealed that female participants scored significantly higher on somatic anxiety (t = -2.21, df = 833, p = 0.028, Cohen's d = -0.155) and worry (t = -3.17, df = 833, p = 0.002, Cohen's d = -0.223) compared to males. In the analysis by sport type, participants engaged in team sports scored significantly higher on somatic anxiety (t = 2.70, df = 833, p = 0.007, Cohen's d = 0.187), Worry (t = 1.97, df = 833, p = 0.049, Cohen's d = 0.136), and concentration disruption (t = 2.73, df = 833, p = 0.007, Cohen's d = 0.189) than those in individual sports. Additionally, in the analysis by grade level, freshman college athletes exhibited significantly lower sport anxiety compared to sophomore athletes [F(4, 830) = 4.06, p = 0.003, =0.019]. The mediation analysis revealed that concentration disruption in sport anxiety is significantly and negatively related to subjective happiness. Additionally, need satisfaction (competence, autonomy, and relatedness) mediates the relationship between worry, as well as concentration disruption in sport anxiety and subjective happiness. Future research should build on the current study by employing longitudinal designs and integrating multiple objective measures to further explore the relationship between sport anxiety and subjective happiness.