Carbonate rocks are widely distributed in Guizhou Province, and under the dissolution and seepage of groundwater, it is easy to cause engineering geological problems such as tunnel water inflow, reservoir leakage, and rock mass instability. In order to study the evolution of the permeability characteristics of layered dolomite under the condition of weak acid water dissolution, the in-house dissolution and permeability tests of different working conditions were carried out by self-made flow dissolution system, supplemented by microscopic tests such as nuclear magnetic resonance, electron microscopy scanning, XRD (X-ray diffraction), etc., to explore the evolution of the dissolution-permeability characteristics of dolomite. The results show as follows. With the increase of confining pressure, the permeability of dolomite decreases, and the permeability of rock samples is more sensitive under low confining pressure. Under weakly acidic conditions, the dissolution of dolomite with bedding dip angles of 67.5° and 90° is more obvious, which is easy to form dissolution pores and dissolution gaps, enhance connectivity, and make the permeate more inclined to flow in the direction of large bedding dip angle, resulting in higher permeability in these directions. The mathematical relationship between the permeability of dolomite rock samples, the permeability confining pressure and the bedding dip angle is established, and the evolution law of permeability is revealed. The dissolution process of dolomite has obvious selectivity, which tends to preferentially dissolve the surface, joints and fractures of the crystal and the edge of the particles, and then gradually develops to the dissolution of matrix particles. Under the combined influence of bedding inclination angle and flow rate, when the reaction is sufficient, the generated reactants accumulate in some pores, resulting in a decrease in permeability. It can be seen that the results of this study have certain significance for the understanding of the evolution law of seepage characteristics of carbonate rocks in karst areas.