This study is to employ the Grey Relational Analysis of Grey System Theory to explore the relationship sequences between the agency budgets of New Taipei City Police Departments and the factors of performing public security cases. An empirical-study result shows that the most significant relationship is found between annual agency budget preparations and actual police force allocation. The rest significance sequences between annual agency budget preparations and the factors of performing public security cases, which are number of seized weapon and drug violation, breaking cases for overall criminal, traffic violations reported, breaking cases for public order violation, breaking cases for economic crimes, and number of rallies and protests overseen by New Taipei City Police Department is the last.