The compression acquisition of mechanical vibration signals can break through the limitation of ShannonNyquist sampling theorem, this method will turn sampling of the signal into the sampling of the information, which effectively solve the problem of traditional sampling methods to generate huge amounts of data as well as does not cause the loss of information. Reconstruction algorithm for vibration signal is a very important part of this technology, it directly affect the reconstruction accuracy of the vibration signal. However, some present typical reconstruction algorithms are universal, it is necessary to do a systematic research on the recovery effect of the mechanical vibration signal. The adaptability analysis of four typical reconstruction algorithm orthogonal matching pursuit(OMP), stagewise orthogonal matching pursuit(StOMP), basis pursuit(BP), gradient projection(GP) is systematically carried out for the reconstruction of the mechanical vibration signal, mainly in two aspects of the reconstruction precision and the reconstruction time. Simulation experiments show that OMP algorithm has low complexity but it is not suitable for the recovery of mechanical vibration signal; StOMP has a faster computing speed and is very suitable for solving large scale problems; Complexity of BP is high, solving speed is slow, but the reconstruction precision is very high; GP has very fast computing speed, but the reconstruction accuracy is poor.