Inter-generational succession in family enterprises influences internal governance models, and their relationship is mediated by the successor's socialization process. Drawing on the enterprise capability theory, the author employed a survey method to examine the relationship between cognitive assets held by family enterprise successors and two governance modes. The findings confirm that tacit knowledge, relational networks, and entrepreneurial spirit among family enterprise successors positively influence their socialization roles, thereby triggering governance adaptation. Specifically, relational governance is continuously strengthened, while contractual governance exhibits an inverted U-shaped trend. Organizational conventions play a positively moderating role in this influencing process. This study extends the application boundaries of enterprise capability theory, deepens the understanding of enterprise cognitive systems, enriches the literature on the relationship between relational and contractual governance, and provides theoretical foundations for inter-generational governance in family enterprises.