The Martian Moons eXploration (MMX) mission is now under study by the Japan Aerospace Exploration Agency (JAXA). Its scope includes the world's first landing on one of the Martian moons, collecting samples from the surface, and returning to Earth. This paper describes the orbit design for MMX. Nominal and backup trajectories for launch in 2024 and 2026 are discussed. The Mars orbit insertion (MOI) sequence using 3-impulse maneuvers is introduced. A new scheme, the robust MOI, is also proposed as a contingency to enhance the robustness of the mission sequence. A method to design a robust MOI trajectory and examples are presented.