Geotechnical engineering generally involves three-dimensional steady seepage problem with free surface. Traditional numerical methods for solving free surface are based on the assumption of continuum, and the pore flow is averaged over the whole area containing solid particles. In fact, water flow can only occur along the pores of porous media. Based on the equivalent principle of head and flow, the equivalent seepage velocity, continuity equation and boundary conditions of the pipe network model were derived by simplifying the pore structure of porous media into a three-dimensional orthogonal pipe network. Based on the local coordinate system, continuous penalty Heaviside function and variational principle, a three-dimensional steady seepage analysis method with free surface was established for equivalent pipe network model. Thus, the three-dimensional seepage problem was simplified to a one-dimensional form, which greatly reduces the difficulty of solving the three-dimensional steady seepage problem with free surface. The effectiveness of the equivalent pipe network model was verified by the three-dimensional free surface seepage analysis of homogeneous right-angle trapezoidal dam. The three-dimensional steady seepage analysis of the left abutment slope of Kajiwa Hydropower Station was carried out. By comparing with the variational inequality method, the equivalent pipe network model can well reflect the seepage field characteristics of the left abutment slope of Kajiwa Hydropower Station, and has strong applicability and high computational efficiency for the seepage problem of 3D complex engineering.