Mirjalili in 2015, proposed a new nature-inspired meta-heuristic Moth Flame Optimization (MFO). It is inspired by the characteristics of a moth in the dark night to either fly straight towards the moon or fly in a spiral path to arrive at a nearby artificial light source. It aims to reach a brighter destination which is treated as a global solution for an optimization problem. In this paper, the original MFO is suitably modified to handle multi-objective optimization problems termed as MOMFO. Typically concepts like the introduction of archive grid, coordinate based distance for sorting, non-dominance of solutions make the proposed approach different from the original single objective MFO. The performance of proposed MOMFO is demonstrated on six benchmark mathematical function optimization problems regarding superior accuracy and lower computational time achieved compared to Non-dominated sorting genetic algorithm-II (NSGA-II) and Multi-objective particle swarm optimization (MOPSO).