In applications of petroleum reservoir problem, it is very important to study the fluid phases within a complicated porous media coupled with conduit systems. Recently, a dual-porosity-Stokes model is developed to simulate the complicated dual-porosity-conduit system which could be used for realistic problems such as shale/tight oil/gas reservoirs. The new model consists of a dual-porosity model to govern the porous media flow and a Stokes equation to control the free flow and coupled via four interface conditions. Such coupled model is usually hard to solve since it will result into a large and complicated system. In this paper, we propose an improved partitioned time stepping scheme to efficiently and accurately solve the large system caused by the coupled dual-porosity-Stokes model.