Time-varying cable-force identification is fundamental for assessing the fatigue damage of stay cables. This study proposes a novel method for real-time time-varying cable force identification. This method updates the cable vibration signals through the sliding window and employs adaptive chirp mode decomposition (ACMD) to identify the instantaneous frequencies of the cables. Finally, the cable forces were calculated based on the taut string theory. The novelty of this study lies in the introduction of ACMD to enhance the accuracy of cable-force identification, while adaptively determining the key parameters of ACMD based on the scale space peak picking (SSPP) algorithm. The effectiveness of this method was been verified through numerical models, with the results showing that the maximum relative error in cable-force identification was 0.87%. Furthermore, this method was successfully applied to a sea-crossing cable-stayed bridge, demonstrating its ability to assess cable force accurately.