The l_(2,1)-norm regularization can efficiently recover group-sparse signals whose non-zero coefficients occur in a few groups. It is well known that the l_(2,1)-norm regularization based on the classic alternating direction method shows strong stability and robustness in many applications. However, the l_(2,1)-norm regularization requires more measurements. In order to recover groupsparse signals with a better sparsity-measurement tradeoff, the truncated l_(2,1)-norm regularization and reweighted l_(2,1)-norm regularization are proposed for the recovery of group-sparse signals based on the iterative support detection. The proposed algorithms are tested and compared with the l_(2,1)-norm model on a series of synthetic signals and the Shepp-Logan phantom. Experimental results demonstrate the performance of the proposed algorithms,especially at a low sample rate and high sparsity level. The l_ (2,1) -norm regularization can efficiently recover group-sparse signals whose non-zero coefficients occur in a few groups. It is well known that the l_ (2,1) -norm regularization based on the classical alternating direction method However, the l_ (2,1) -norm regularization requires more measurements. In order to recover groupsparse signals with a better sparsity-measurement tradeoff, the truncated l_ (2,1) -norm regularization and reweighted l_ (2,1) -norm regularization are proposed for the recovery of group-sparse signals based on the iterative support detection. The proposed algorithms are tested and compared with the l_ (2,1) -norm model on a series of synthetic signals and the Shepp-Logan phantom. Experimental results demonstrate the performance of the proposed algorithms, especially at a low sample rate and high sparsity level.