In this paper,we investigate truncated e2/e1-2 minimization and its associated alteating direction method of multipliers (ADMM) algorithm for recovering the block sparse signals.Based on the block restricted isometry property (Block-RIP),a theoretical analysis is presented to guarantee the validity of proposed method.Our theoretical results not only show a less error upper bound,but also promote the former recovery condition of truncated e1-2 method for sparse signal recovery.Besides,the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.