Navier Stokes/Darcy equation can be used to simulate the pollution of pollutants in rivers to groundwater, and the penetration of blood in blood vessels and organs. Due to its wide applications in practice, the research on the numerical method for Navier Stokes/Darcy equations has attracted extensive attention. A BDF2 modular gradient divergence stablized numerical scheme for solving Navier Stokes/Darcy equations is proposed. This scheme improves the validity and accuracy of the solution by adding a stabilization term. While retaining the advantages of the gradient divergence stable scheme, it can effectively avoid bad effects caused by large stabilization parameters. The stability and error analysis of the scheme are given. Finally, the correctness of the theoretical analysis is verified by numerical examples.