Despite several missions, the origin of the two Martian moons, Phobos and Deimos, remains an open question. The goal of the next JAXA’s flagship mission Martian Moons eXploration will be to explore the two Martian moons. The satellite will be injected into a quasi-satellite orbit and it will require some station-keeping maneuvers to maintain the satellite on these orbits. Traditional methods for station-keeping around libration points are not applicable for these orbits due to their rapid evolution. In this paper we propose a new approach to perform station-keeping on periodic and quasi-periodic orbits based on convex optimization. Successive convex optimization is used to solve the time free fuel optimal problem to drive the satellite back to a reference trajectory. The latter is updated every GNC (Guidance Navigation and Control) loop by means of an innovative Discrete Fourier Transform approach that exploits the periodicity and quasi-periodicity of quasi-satellite orbits. To assess the robustness of the methodology the control and the references are computed in the autonomous dynamical model while the propagation is performed in the non-autonomous model while adding injection, orbit determination and executions errors. Monte Carlo analysis demonstrate that quasi-satellite orbits can be maintained using less than 6 m/s per month.