In this paper, we consider the decoupled stabilized finite element method for the dual-porosity-Navier-Stokes model coupling the free flow region and the microfracture-matrix system by using four interface conditions on the interface. The stabilized finite element method is decoupled in two levels, and it allows the coupling problem to be divide into three subproblems in a non-iterative manner, which improves the computational efficiency. In addition, the stability and convergence of the decoupling scheme are also analyzed. Finally, the theoretical results are illustrated by some numerical experiments. KEYWORDS convergence, decoupled method, dual-porosity-Navier-Stokes, finite element method, numerical experiments, stability 1 INTRODUCTION Many scientists and engineers have investigated the fluid flow interaction between conduit and porous media region [1-3]. A large number of practical problems, such as groundwater flow system, interaction between surface, and groundwater flow, biochemical transportation, blood flow in artery, vein, and so forth [4-7], have been established relevant hydrodynamic models by scientists. In addition, a lot of efforts have been devoted to develop appropriate numerical methods to solve the Stokes-Darcy fluid system, including the coupled finite element methods [8-10], domain decomposition methods [11-13], the Lagrange multiplier method [14, 15], and so forth. Although the traditional Stokes-Darcy model [16-18] has been well studied, it has some limitations in describing the heterogeneity of porous media. It is worth noting that the real natural fractured