Dielectric breakdown of BST thin films prepared by RF sputtering is studied in this paper. It is found that, the BST thin films will have already broken before the voltage reaches to conventional breakdown strength, which is normally tested by ramping the voltage and recording the voltage at which an abrupt rise in leakage current is observed. Accordingly, another state of BST thin films, i. e. the incipient breakdown, is found instead. The model which describes the films' configuration changes with the increase of voltage is established, and a new method to determine the practical breakdown strength is proposed.