In this paper, we focus on a linearly constrained composite minimization problem whose objective function is possibly nonsmooth and nonconvex. Unlike the traditional construction of augmented Lagrangian function, we provide a proximal-perturbed augmented Lagrangian and then develop a new Bregman Alternating Direction Method of Multipliers (ADMM). Under mild assumptions, we show that the novel augmented Lagrangian residual can be bounded by the primal residuals plus a summable sequence. We further demonstrate that the augmented Lagrangian sequence converges to the limitation of objective sequence, and the iterative sequence converges to a stationary point of the problem. The sublinear convergence rate of the primal residuals are also established.