In underground engineering, the fracture dip angle and three-dimensional stress have great influence on the permeability and mechanical properties of fractured rock mass. Firstly, single-fracture samples with similar three-dimensional fractal dimensions and different dip angles were selected by using CT scanning technology. Then, the grouting material seepage tests under different dip angles and different three-dimensional stresses were carried out by self-developed single-fracture stress-seepage coupling true triaxial test system. The experimental data of stress-strain curve, grouting pressure, and grouting material flow rate of single-fracture specimen under different fracture dip angles and three-dimensional stress were obtained. The results show that the three-dimensional fractal dimension can be used as an index to measure the influence of fracture factors on grouting seepage test. The third principal stress σ 3 had a greater influence on the fracture width than the first principal stress σ 1 . The larger the fracture inclination, the lower the strength of the single-fracture specimen. As the third principal stress σ 3 increases, the grouting pressure increased while the grouting flow decreased. With the increase of the fracture inclination angle, the influence of σ 1 on the hydraulic conductivity became larger, while the influence of σ 3 on the hydraulic conductivity became smaller. Moreover, the expression of hydraulic conductivity of single-fracture specimen with different dip angles under three-dimensional stress was obtained by nonlinear fitting of hydraulic conductivity data.