Excitons in monolayer transition metal dichalcogenide (TMD) provide a paradigm of composite Boson in 2D system. This letter reports a photoluminescence and reflectance study of excitons in monolayer molybdenum diselenide (MoSe2) with electrostatic gating. We observe the repulsive and attractive Fermi polaron modes of the band edge exciton, its excited state and the spin-off excitons. Our data validate the polaronic behavior of excitonic states in the system quantitatively where the simple three-particle trion model is insufficient to explain.