We propose to discover approximate primary functional dependency (aPFD) for web tables, which focus on the determination relationship between primary attributes and non-primary attributes and are more helpful for entity column detection and topic discovery on web tables. Based on association rules and information theory, we propose metrics Conf and InfoGain to evaluate PFDs. By quantifying PFDs' strength and designing pruning strategies to eliminate false positives, our method could select minimal non-trivial approximate PFD effectively and are scalable to large tables. The comprehensive experimental results on real web datasets show that our method significantly outperforms previous work in both effectiveness and efficiency.