In this work, we consider the inverse spectral problem for the impulsive Dirac systems on (0,π) with the jump condition at the point π2. We conclude that the matrix potential Q(x) on the whole interval can be uniquely determined by a set of eigenvalues for two cases: (i) the matrix potential Q(x) is given on 0,(1+α)π4; (ii) the matrix potential Q(x) is given on (1+α)π4,π, where 0α1.
