  Compressed sensing shows that a sparse signal can stably be recovered from
incomplete linear measurements. But, in practical applications, some signals
have additional structure, where the nonzero elements arise in some blocks. We
call such signals as block-sparse signals. In this paper, the
$\ell_2/\ell_1-\alpha\ell_2$ minimization method for the stable recovery of
block-sparse signals is investigated. Sufficient conditions based on block
mutual coherence property and associating upper bound estimations of error are
established to ensure that block-sparse signals can be stably recovered in the
presence of noise via the $\ell_2/\ell_1-\alpha\ell_2$ minimization method. For
all we know, it is the first block mutual coherence property condition of
stably reconstructing block-sparse signals by the $\ell_2/\ell_1-\alpha\ell_2$
minimization method. Additionally, the numerical experiments implemented verify
the performance of the $\ell_2/\ell_1-\alpha\ell_2$ minimization.
