A new primal-dual path-following shifted penalty-barrier method will be described for solving nonlinear inequality constrained optimization problems (NIP). The proposed method has a bi-level structure in which a trajectory parameterized by the penalty and barrier parameters and Lagrangian multipliers estimates is closely followed towards a constrained local minimizer of NIP. This method inherits some features of the primal-dual augmented Lagrangian method for solving nonlinear equality constraint problems (NEP) but has been extended to handle inequality constraints. Global and local convergence results will be presented. Finally, numerical results from the CUTEst test collection will be provided to support the robustness of the proposed algorithm.