Explaining the causes of infeasibility of Boolean formulas has many practical applications in electronic design automation and formal verification of hardware. Furthermore,a minimum explanation of infeasibility that excludes all irrelevant information is generally of interest. A smallest-cardinality unsatisfiable subset called a minimum unsatisfiable core can provide a succinct explanation of infea-sibility and is valuable for applications. However,little attention has been concentrated on extraction of minimum unsatisfiable core. In this paper,the relationship between maximal satisfiability and mini-mum unsatisfiability is presented and proved,then an efficient ant colony algorithm is proposed to derive an exact or ncarly exact minimum unsatisfiable core based on the relationship. Finally,ex-perimental results on practical benchmarks compared with the best known approach are reported,and the results show that the ant colony algorithm strongly outperforms the best previous algorithm.