Fractures significantly change the hydraulic and transport properties relevant to underground and marine engineering activities. This paper proposes a 3D digital voxel-based method to rapidly construct a fracture model from a fractured sample and to study the fracture flow characteristics. Single-phase laminar flow is simulated to study the hydraulic transport properties and fluid flow in single fractures from different projection directions. The hydraulic head distributions in fractures strongly depend on the injected hydraulic head and the locations of the given points in the fractures. The hydraulic conductivity is highly dependent on the fracture aperture and increases with increasing fracture aperture. Large differences in fracture flow are observed in the extracted fractures from different projection directions, and the relative errors between the experimental and numerical hydraulic transmissivity results considering the full fracture plane are all less than those considering the other planes evaluated, and they are less than 5%. Thus, the full fracture plane is more effective for evaluation of the hydraulic and transport properties of fractures in rocks due to the comprehensive consideration of the fracture shape from different projection directions and fracture aperture in different positions.