Cross-chain swaps have emerged as a critical and indispensable blockchain application, expanding the circulation scope of digital assets from a single chain to multiple chains, thus improving their flexibility and usability. Atomic swap acts as the key technology for achieving cross-chain swaps without the need for cross-chain infrastructures or trusted third parties. However, existing atomic swap solutions suffer from the lockup griefing problem, which prevents fast settlement of parties’ assets when a swap is cancelled midway. While some research works provide solutions to compensate parties experiencing lockup griefing, there is currently no work focusing on preventing lockup griefing through mechanism design. To fill the gap, this paper introduces a novel atomic cross-chain swap protocol, called Fast Settlement Swap (FS-Swap). By analyzing the fundamental causes of lockup griefing, FS-Swap provides a mechanism design that prevents the occurrence of lockup griefing in the first place. The experimental results demonstrate that, when a swap is cancelled midway, FS-Swap significantly reduces asset locking time by over 99% compared to existing atomic swap solutions, decreasing it from several hours to less than 2.1 min.