In this paper, we investigate the nonlinear system of Navier-Stokes and Darcy flows coupled by the Beavers-Joseph-Saffman law on the interface. The wellposedness of the weak and numerical solutions are established. Mortar elemen method is introduced to solve the coupled model. Error estimates are derived for the proposed method. We adopt an iterative algorithm to solve the nonlinear scheme generated by the coupled system. Numerical example is provided to verify the theoretical analysis.