In this paper, we propose a majorized Newton-CG augmented Lagrangian-based finite element method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented Lagrangian method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults. The 3D restoration problem is reformulated to a constrained optimization problem.We apply the majorized Newton-CG augmented Lagrangian method to solve the problem.This approach can be used to solve large-scale 3D restorations of geological models.Numerical results show the efficiency of the cases with complicated faults.