This study combines the SC-E model and entrepreneurial bias research to formulate a “social capital-cognitive bias-entrepreneurial intentions framework,” and to discuss the differences between gender in the relationship among social capital, cognitive bias, and entrepreneurial intentions. Additionally, it also explores the mediation effects of optimism and overconfidence. Structural equation modeling is used to examine the hypotheses on a sample of 511 students at a Taiwanese university. Empirical results show that neither bonding nor bridging social capital has a direct impact on entrepreneurial intentions. They also indicate that male students are more optimistic and have higher entrepreneurial intentions than females. Regarding the mediation effect, bridging social capital may evoke both optimism and overconfidence, but bonding social capital only affects optimism. Furthermore, optimism is the antecedent of overconfidence, and it creates another channel of the mediation effect.