At present, the sparse recovery problem is mainly solved by convx optimization algorithm and greedy tracking method. However, the former has defects in recovery efficiency and the latter in recovery ability, and neither of them can obtain effective recovery under large sparsity or small observation degree. In this paper, we propose a new sparse recovery algorithm based on arithmetic optimization algorithm and combine the ideas of greedy tracking method. The proposed algorithm uses arithmetic optimization algorithm to solve the sparse coefficient of the signal in the transform domain, so as to reconstruct the original signal. At the same time, the greedy tracking technique is combined to design the initial position of the operator before solving, so that it can be searched better. Experiments show that compared with other methods, the proposed algorithm can not only obtain more effective recovery, but also run faster under general conditions of observation number. At the same time, It can also recover the signal better in the presence of noise.