As subspace pursuit algorithm under cosparsity analysis model in compressed sensing has the shortcomings of low completely successful reconstruction probability and poor reconstruction performance, a cosparsity analysis subspace pursuit algorithm was proposed. The proposed algorithm was realized by adopting the selected random compact frame as the analysis dictionary and redesigning target optimization function. The selecting method of cosparsity value and the iterated process were improved. The simulation experiments show that the proposed algorithm has obviously higher completely successful reconstruction probability than that of Analysis Subspace Pursuit (ASP) and other five algorithms, and has higher comprehensive average Peak Signal-to-Noise Ratio (PSNR) for the reconstructed signal than that of ASP and other three algorithms, but a little bit lower than that of Gradient Analysis Pursuit (GAP) and other two algorithms when the original signal has Gaussion noise. The new algorithm can be used in audio and image signal processing.