The relationship between family science capital and students' science career intentions has been widely discussed since the ASPIRES project initially proposed this linkage. Since science capital is more likely to be clustered in some social groups, the linkage between family science capital and their children's science aspirations may exacerbate the inequality of science capital between the advantaged and disadvantaged groups. The present study investigates the mechanism of the transformation process from students' family science capital to their science career intentions, which sheds light on the process of the inter-generational transmission of science capital. This study has recruited 1161 Chinese high school students. By employing the structural equation modelling method, this study supports that family science capital acts as a distal facilitator but not a direct proximal support contributing to students' science career intentions. The influence of family science capital on students' perceptions of science is a long-term infiltration that is embedded in students' daily life and contributes to students' science-related positive learning experiences and interest in science. However, family science capital does not directly predict students' science career intentions. This result implies that without the long-term infiltration of science embedded in daily life, students are less likely to choose science just due to having vocational guidance or knowledge support in science from family.