Abstract：The filtering flow in the core of low-permeability does not follow Darcy's law. There is a starting pressure in the filtering flow, and the porous flow curve is no longer a straight line. Some improvements on the existing core flooding experiments and methods of measurement are proposed in this paper to obtain the non-linear filtering flow curves. The low-velocity flow characteristics in a glutenite with high contents of clay-swelling minerals were studied by using the improved experimental device. The experimental curves do not pass the origin of the coordinate system, with an intercept in the pressure axis. There are two types of filtering flow curves: the upward bending curves and the downward bending curves. The tiny throat size and high heterogeneity of rock in a low permeability reservoir are the causes to make the flow non-linear. The reservoir lithology is also responsible to the nonlinearity. The cores used in experiments with a high content of clay minerals including illite/smectite formation and illite have a significant effect on the effective permeability. Based on the theories of the seepage flow model, taking account of the throat radius, with the clay-swelling ability as a target, a preliminary study is carried out on the mechanism of different nonlinear flow curves. The final results show that the clay-swelling reduces the size of the throat participated in seepage, and as a result, reduces the velocity and increases the starting pressure, which accounts for the upward bending of the nonlinear flow curves.