Continuous flash suppression (CFS) refers to a technique to render a monocular stimulus invisible by presenting a dynamic series of high-contrast patterns (such as Mondrian patterns) to the other eye. Despite its popularity as a tool to suppress stimulus from awareness, the suppression mechanisms underlying CFS remain not well understood. To further elucidate the suppression mechanisms, this study investigated the effects of eye swapping on CFS suppression by manipulating the eye of presentation of the suppressor and the target. Results showed that eye swapping of the suppressor and the target significantly reduced the strength of CFS suppression when swapping frequency was higher (3.5 Hz). However, strong suppression persisted at lower swapping frequency (1.2 Hz). Investigation of the time course of suppression revealed that suppression was weaker just after eye swapping but that it quickly regained strength over the monocular presentation period of the suppressor. However, this buildup seemed to not be fast enough to closely follow eye swapping at higher frequency. These findings can be better understood by the contribution of monocular processes to CFS suppression. They imply that interocular suppression caused by competition between monocular processes can mediate phenomenal suppression over multiple eye swaps when swapping frequency is low. The significance of the findings is discussed in relation to binocular rivalry and binocular switch suppression.