This work discusses on designing fast and efficient Mars escape trajectory for Martian Moons eXplorer in the three-body system using chemical and electric propulsion. Chemical propulsion is used for fast low-energy escape from Mars and electric propulsion is used to increase v-infinity and to re-encounter with Mars for a gravity assist. We propose a method called “all-three-body method" and we compare the new method with the patched three-and-two-body method, and a parametric study is carried out. Using electric propulsion soon after Mars escape injection done by chemical propulsion, the all-three-body method would consume less fuel than patched three-and-two-body method. Limiting the use of chemical propulsion could also increase the final spacecraft mass when electric propulsion is used within 10 days after impulsive maneuver.