This paper proposes a new approach which applies Cantor-like search strategy to computing critical clearing time (CCT) after searching the initial search interval of fault clearing time (FCT) by advance-and-retreat predictor-corrector technology. On the basis of discussing the mathematical nature of computing CCT based on time-domain simulation, the work started with the comparison of conventional computer linear optimization search strategies, then combined Cantor-like search with transient stability analysis feature and realized CCT rapid calculation with the classical Dichotomy substituted. Simulations on New England 10-generator 39-bus system demonstrate that this new algorithm has a good advantage over efficiency and precision, as well as its engineering application prospect.