In order to solve the issue of the deterioration of reconstruction performance in compressed sensing(CS) for acceleration signal with poor sparsity that is produced by noise, this paper proposed a new method for perfect reconstruction of acceleration signal by using empirical mode decomposition(EMD) and wavelet denoising. Its basic idea is that the best sparsity of acceleration signal is firstly gained by using EMD and wavelet threshold denoising method. And then, considering CS and acceleration signal with block structure, block sparse Bayesian learning algorithm is applied to perfectly reconstruction original acceleration signal. The acceleration signal from human activity dataset USC-HAD is selected to test the effectiveness of the proposed method. The experimental results show that when compared to traditional CS algorithm without pre-denoising processing, the proposed method can obtain the best value of signal-to-noise ratio and root mean square error. Also, these results suggested that our proposed method has the superior ability of denoise for gaining best sparsity of acceleration signal, which significantly improve the reconstruction performance of CS.