Nowadays, the propellant consumption minimization is a fundamental task for space missions in order to save more money budget and to plan a longer duration for them. In the last years space technology has moved forward, overcoming classical astrodynamics methods as the Lambert's problem solution and the Hohmann transfer which are ideal and open-loop maneuvers that require a strong human effort. As it has been seen in control system literature, a MPC-based control strategy is a very interesting solution because allows us to deal with linear and nonlinear systems, to impose input and/or state constraints, to have a guidance and control strategy managed by a single algorithm and most important to have an optimum trade-off between performances and fuel consumption.