The block orthogonal matching pursuit (BOMP) algorithm is an efficient method in compressed sensing (CS) for the reconstruction of block‐sparse signals, whose non‐zero entries occur in clusters. However, due to the non‐ideal factors in practice, there exits perturbation in the CS system, which may cause significant performance degradation during reconstruction. In this Letter, a perturbed BOMP algorithm is presented to deal with this problem, which extends BOMP algorithm to the perturbation case. The proposed algorithm performs controlled perturbation on each selected block of support vectors to decrease the orthogonal residual at each iteration. Moreover, the condition of successful reconstruction is derived. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm.