In this paper, a non-linear stochastic model was constructed to introduce psychological capital as a random disturbance and predict students’ entrepreneurial intentions. Then, we conducted a differential analysis of students’ psychological capital on indicators of gender, family economic status and parents’ attitudes toward their children’s entrepreneurship, and also tested the mediating effects of innovation efficacy and perceived behavioral control to reveal the inner mechanism of the psychological capital of college students’ innovation and entrepreneurship. Finally, a psychological support system for college students’ entrepreneurship was constructed, including three dimensions a positive organizational system, positive emotional experience, and positive personality traits. The study showed that the direct effect of psychological capital on entrepreneurial intention was significant, β = 0.15, t = 3.19, p < 0.01, and overall significant. Innovative efficacy significantly and positively predicted perceived behavioral control β=0.48, t=12.67, p<0.001 and entrepreneurial intention β=0.09, t=2.15, p<0.05. This study has important implications for improving the quality of entrepreneurial activities and optimizing the entrepreneurial environment of college students.