In this paper, we consider the defocusing coupled nonlinear Schr¨odinger equation (dCNLS) and derive generalized localized wave solution formula through Darboux transformation method (DT). It’s well known that the nonlinear Schr¨odinger equation (NLS) is an important model in mathematical physics, which can be applied to hydrodynamics, plama physic, molecular biology and optics. The coupled nonlinear Schr¨odinger equation (CNLS) is an extension of NLS and its localized wave solutions are more colorful and complicated. Recently, there ara many works about focusing CNLS through DT. For instance, rogue wave solution, bright-dark-rogue wave solution and high order solutions have been given. However, for the dCNLS the Darboux matrix no longer keeps positive or negative definite, so it’s difficult to derive meaningful localized wave solutions through DT. In this work, we use the matrix analysis method to deal with this problem. Firstly, we derive the DT through loop group method for dCNLS. Secondly, we take plan wave functions as the seed solutions. When Im(λ1) = 0, we can obtain the dark-dark soliton solutions. When Im(λ1) 6= 0, we classify three different cases to discuss it. The first case is a2 = a1. In this case, we obtain degenerate breather and bright-dark soliton. The second case is a2 6= a1. In this case, we can obtain the general breather solution and general rogue wave solution. Lastly, we derive general N-fold DT in terms of determinant and give the interaction between different types of solutions. These result would be helpful for nonlinear localized wave excitations and applications in vector nonlinear systrms.