For many physical phenomena, it is necessary to establish wave models with two or more components to explain different patterns, frequencies and polarization phenomenna. In addition, only multi-component systems can explain the energy exchange of multiple physical fields theoretically and practically. Therefore, for a integrable system, how to construct a non-trivial differential equation system that is integrable and contains the original system as a subsystem is one of the important problems in the study of integrable coupling. In this work, the integrable couplings of the Ablowitz-Kaup-Newell-Segur equation are constructed based on a stationary equation. Then a Darboux transformation in which the elements can be expressed by the quotient of two determinants is obtained, and the production process is proved strictly. By comparing the forms and characteristics of the one-fold Darboux transformation, $N$-fold Darboux transformation formula which can be demonstrated as determinants is derived. Therefore, by means of seed solutions and $N$-fold Darboux transformation, any-order soliton solutions can be derived. As the application of Darboux tarnsformation, we solve the exact explicit one-soliton solutions.