In high-end equipment applications, face gears are gradually replacing bevel gears as a new solution for crossed-axis transmission due to the compact size and lightweight advantages of their transmission systems. However, under harsh service conditions, wear remains the primary cause of failure. This paper establishes a mathematical model of face gears based on virtual machining principles and conducts Loaded Tooth Contact Analysis (LTCA). A UMESHMOTION subroutine within Abaqus is developed to embed the Archard wear model into the finite element constitutive framework. To address edge nodes on the complex tooth surface, coordinate transformation is applied, and an Arbitrary Lagrangian-Eulerian (ALE) adaptive mesh technique is integrated. A mesh reconstruction-based numerical simulation method for face gear tooth surface wear is proposed, characterized by high convergence and precision. The simulation calculates the distribution of contact stress, relative sliding, and wear on the tooth surface of face gear. It is found that the wear depth decreases from the tooth tip to the root and then increases. The central region of the contact path remains in a pure rolling state, with no wear observed.