In this talk, we propose and analyze domain decomposition methods to decouple the large system arisen from the dual-porosity-Stokes model. The recently developed model describes a complicated dualporosity-conduit system which uses a dual-porosity/permeability model to govern the flow in porous media coupled with free flow via four physical interface conditions. First of all, Robin boundary conditions are applied to decouple the coupling conditions on the interface. Then, Robin-Robin domain decomposition methods are established based on the two decoupled sub-problems. Convergence analysis is demonstrated and a geometric convergence order is obtained. Optimized Schwarz methods are proposed for the dual-porosity-Stokes model and optimized Robin parameters are derived to improve the convergence of proposed algorithms. Numerical experiments are presented to illustrate the accuracy and applicability of the proposed algorithms.