In the paper, an iterative group sparse channel estimation and decoding algorithm is proposed for OFDM communication systems. The group basis pursuit de-noising (Group-BPDN) method based on the group sparsity of wireless multipath channel is used in channel estimation to improve the performance. Moreover, the soft-output viterbi algorithm(SOVA) method is used for channel decoding. The most reliable decoding data are fed back to the input of channel estimator. Consequently, the new set of known signals is constituted by the feedback data and pilot. Therefore, during iterative process, the known information used in the sparse recovery is increased, which can improve the performance of sparse recovery. Furthermore, the noise power which is useful for sparse recovery is estimated through the new set of known signals and the channel response is estimated. The simulation results demonstrate that the proposed algorithm improves the channel estimation performance and reduces the error rate.