Abstract: The complicated mass and momentum transfer problems in the porous region,especially at the interface between porous and free fluid region were analyzed in an asymmetric and coupled porous-fluid channel. By taking the Brinkman-extended Darcy model in the porous region with the velocity continuity and the shear stress jump interface conditions, the fluid transfer characteristics were solved. The analytical expressions for the fluid flow velocity of each region and friction coefficient in the coupled asymmetric channel were proposed by considering the stress jump interfacial condition. Then the effects of interfacial stress jump coefficient, Darcy number and dimensionless off-center thickness of porous layer on fluid flow velocity and friction coefficient were studied. The results show that under certain conditions changing the interface property can obviously control the velocity profile in each region of the coupled channel. For certain values of Darcy number and porous off-center thickness, increasing the interfacial stress coefficient has a reducing effect on the interfacial velocity but an increasing effect on the fluid friction coefficient, and the effect is more obvious when the interfacial stress coefficient is less than 0, in this case that without considering the effect of the interfacial stress coefficient can cause larger error. When both the interfacial stress coefficient and the porous off-center thickness are smaller negative values, the effect by varying the porous off-center thickness on the interfacial velocity is greater than the effect of altering the interfacial stress coefficient, while when the interfacial stress coefficient and the porous off-center thickness of porous layer are larger positive values, the result is quite the opposite. At a larger Darcy number, both the interfacial stress coefficient and porous off-center thickness have greater influence on the fluid friction coefficient; reducing Darcy number to a certain small value, the influence of interfacial stress coefficient on fluid friction coefficient can be neglected and the fluid friction coefficient is only related to the porous off-center thickness, and much more sensitive to a larger porous off-center thickness.