This paper presents the conceptual design of the IMaGInE (Innovative Mars Global International Exploration) Mission. The mission's objectives are to deliver a crew of four astronauts to the surface of Deimos and perform a robotic exploration mission to Phobos. Over the course of the 343 day mission during the years 2031 and 2032, the crew will perform surface excursions, technology demonstrations, In Situ Resource Utilization (ISRU) of the Martian moons, as well as site reconnaissance for future human exploration of Mars. This mission design makes use of an innovative hybrid propulsion concept (chemical and electric) to deliver a relatively low-mass reusable crewed spacecraft (approximately 100 mt) to cis-martian space. The crew makes use of torpor which minimizes launch payload mass. Green technologies are proposed as a stepping stone towards minimum environmental impact space access. The usage of beamed energy to power a grid of decentralized science stations is introduced, allowing for large scale characterization of the Martian environment. The low-thrust outbound and inbound trajectories are computed through the use of a direct method and a multiple shooting algorithm that considers various thrust and coast sequences to arrive at the final body with zero relative velocity. It is shown that the entire mission is rooted within the current NASA technology roadmap, ongoing scientific investments and feasible with an extrapolated NASA Budget. The presented mission won the 2016 Revolutionary Aerospace Systems Concepts - Academic Linkage (RASC-AL) competition.