This thesis describes the research I did during my Master's study. I investigated the stau-neutralino coannihilation region of the Mirage Mediation Model at the Large Hadron Collider (LHC). By constructing five kinematic observables at the LHC, the masses of supersymmetric particles (sparticles) were determined. The Mirage Mediation Model parameters were determined from the sparticles' masses. This is the first time to establish the Mirage Mediation Model at the LHC. All these techniques can be applied to other coannihilation regions of the Mirage Mediation Model and other supersymmetry (SUSY) models.