This paper focused on the robust stability of switched Boolean networks (SBNs) subject to external disturbances and one-bit function perturbation. The reachable sets of a perturbed state before and after function perturbation were constructed, and some basic properties of these reachable sets were presented. Based on the reachable sets of a perturbed state, a necessary and sufficient condition was proposed to verify the robust stability of SBNs with one-bit function perturbation.