This paper considers the problem of suppressing complex-jamming, which contains multiple near-mainlobe jammings (multi-MLJs) and self-defensive jamming (SDJ). The complex-jamming can also be divided into blanket jamming which considers multiple near-mainlobe blanket jammings, and deception jamming which considers dense false-target jammings (DFJs), containing self-defensive DFJ and multiple near-mainlobe DFJs. We propose a space-time complex-jamming suppression algorithm based on blind source separation (BSS). A space-time model is established, which consists of spatial four beams and temporal two adjacent pulse repetition intervals (PRIs). Then the mixed signal from space-time channels can be separated by the BSS technology. Finally, the target can be obtained by the pulse compression approach. Hence, the complex-jamming can be suppressed in the view of BSS. The new algorithm does not require priori knowledge about all the source signals, which is easy to implement for engineering applications.