When noisy signals from a Micro-electromechanical System(MEMS) gyro are reconstructed by wavelet decomposes, it is difficult to choose the wavelet coefficients corresponding to the real signals. Therefore, a kind of Layerwise and Adaptive Matching Pursuit-based(LAMP-based)algorithm was proposed to solve the problem mentioned above. A sparse extraction construction of wavelet coefficients from the real MEMS gyro signal was established by recovering the sparsity of the wavelet coefficients of the noisy gyro signal. Then, the new LAMP algorithm was designed to pick out the most sparse wavelet coefficients among all wavelet coefficients of the noisy MEMS gyro signal, and the chosen wavelet coefficients were utilized to reconstruct the real MEMS gyro signal. Substantial experiment results indicate that the proposed LAMP algorithm is superior to other iterative greedy reconstruction algorithms. It effectively removes substantial MEMS gyro noise, and corresponding azimuth average error reduces from 10.060 2 （°）/h (before LAMP reconstruction) to 5.034 6 （°）/h (after LAMP reconstruction), which shows its denoising performance to be better than that of the traditional wavelet threshold reconstruction method with an azimuth average error of 8.596 8 (°)/h(after wavelet threshold reconstruction). It concludes that the proposed LAMP-based signal reconstruction method for MEMS gyro has good application prospect.