This paper studies the precoding optimization problem for Extremely Large-Scale Multiple-Input-Multiple-Output downlink systems under a near-field channel model based on spectral efficiency fairness. The near-field channel model considers the coexistence of line-of-sight (LOS) and non-line-of-sight (NLOS) non-stationary mixed channels within the cell, where LOS channels are modeled using spherical wave models, while NLOS channels are modeled using Rayleigh models. The geometric mean of spectral efficiency is used as the optimization target to ensure fairness among users and optimize the overall spectral efficiency of the system. To handle the complex optimization objective function, a first-order Taylor expansion approximation is applied to create a simplified objective function; subsequently, Lagrangian dual transformation and quadratic transformations are used to transform the original optimization problem into an equivalent one that is easier to solve. Finally, to reduce computational complexity, the Projection Fast Iterative Shrinkage Threshold Algorithm (PFISTA), which combines fast iterative shrinkage thresholding algorithms with projected gradient descent, is employed to solve the equivalent optimization problem. Simulation results show that using the geometric mean as the objective function can reduce differences in spectral efficiencies among users, leading to a balanced improvement in user spectral efficiencies. Moreover, PFISTA achieves comparable performance to existing methods while maintaining lower computational complexity.