In this paper, we propose real-time optimal guidance for aircraft terrain-following. Terrain-following is an essential technique for military aircraft and should be carried out in a safe flight while maintaining the lowest altitude as possible. To this end, it must be able to generate the optimal terrain-following guidance command while being robust to disturbances such as wind. In this work, we propose a model predictive control method that performs real-time optimization for terrain-following guidance. MPC reflects the model of the aircraft and several maneuver constraints, so optimal planning for terrain-following can be designed. The nonlinear kinematic model of the aircraft is defined, and successive convexification is performed to linearize the nonlinear model and successfully solve the optimization problem. The proposed algorithm was compared with the general guidance algorithm, in this work we compared it with the L1 navigation law. As a result of real-time simulations, the MPC guidance algorithm performed terrain-following with a safer and smaller error, even with the presence of disturbances.