This article proposes and analyzes a multi-physics domain decomposition method for the steady-state Navier-Stokes-Darcy model with three interface conditions. In addition to the regular interface condition for the mass conservation and the force balance, Beavers-Joseph condition is used as the interface condition in the tangential direction. The major mathematical difficulty in adopting the Beavers-Joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system. The wellposedness of this system is showed by using a branch of non-singular solutions. The three physical interface conditions are utilized together to construct the Robin type boundary conditions on the interface and decouple the two physics which are described by Navier-Stokes and Darcy equations respectively. Then the corresponding multi-physics domain decomposition method is proposed and analyzed. Numerical results using finite elements are presented to illustrate the features of the proposed method.