Numerical simulation of wetting or dewetting processes is challenging due to the multiscale feature of the moving contact line. This paper presents a numerical method to simulate three-dimensional wetting processes in the framework of lubrication equation and Navier slip condition. A mesoscopic model of the moving contact line is implemented with a cutoff of the computational domain at a small distance from the contact line, where boundary conditions derived from the asymptotic solution of the intermediate region are imposed. This procedure avoids the high resolution required by the local interface near the contact line and enables the adoption of physically small slip lengths. We employ a finite element method to solve the lubrication equation, combined with an arbitrary Lagrangian-Eulerian method to handle the moving boundaries. The method is validated by examining the spreading or sliding of a liquid drop on the wall. The numerical results agree with available exact solutions and approximate theories.