Abstract We consider the compressive sensing reconstruction for vibration signals, which are complex due to the harsh working environment. The recent fast iterative shrinkage-thresholding algorithm (FISTA) has paved the way for the signal reconstruction with a low complexity and high efficiency. Unfortunately, when extending to the vibration signals, the current algorithm still has some drawbacks such as the bad reconstruction effect. In this paper, we propose the improved fast iterative shrinkage-thresholding algorithm (IFISTA) to improve the reconstruction effect. Under the new scheme, the reconstruction is promoted by extracting information from the unstable signals in the process of iteration. Then the feature coefficients will be protected from shrinkage during iteration. The effectiveness of the IFISTA is verified by simulated signals and acquired signals. It is showed that the proposed scheme has superior performance in reconstruction and feature protection for vibration signals.