The most commonly used methods to solve contact problems, including the Lagrangian, penalty, and augmented Lagrangian methods, utilize forces to establish equilibrium while ensuring that geometric admissibility is maintained. The contribution at hand aims at a numerical method to describe frictional contact using a displacement-driven approach [1], which is considered a stable alternative. The proposed contact formulation is implemented into the finite element framework for quasi-static loading. The current implementation solves for the contact between rigid and deformable bodies in finite deformation. Constant friction behavior between surfaces in contact is assumed by incorporating Coulomb's friction law. This algorithm is expected to have a higher accuracy compared to the penalty method as it achieves the exact geometric non-penetration condition, similar to the Lagrangian contact method. Moreover, no additional parameter is required in this method. Thus, an ill-conditioned stiffness matrix is avoided. However, linearization of the residual equations results in a nonsquare matrix. Hence, in this work, the singular value decomposition technique is employed to solve this issue, which may increase the computation costs, depending on the size of the problem. Another method that imposes the displacement boundary condition due to contact is the well-known Nitsche's method. Despite having the same displacement approach, the main idea differs. Various numerical examples are presented to demonstrate the numerical method's applicability for different contact mechanics tasks. First, the presented examples verify the displacement-driven approach by investigating its convergence behavior and consistency. Next, the accuracy of the proposed algorithm is validated by the analytical solution of the Hertzian contact and penalty method. Further, the stick and slip condition of large sliding motion in a frictional contact problem under different coefficients of friction is successfully depicted.