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Long-period grating (LPG) fabricated in a graded-index multimode fiber (MMF) by deforming the geometry of the fiber periodically with a focused CO2-laser beam is reported. The effects of the grating parameters on the transmission of the grating are investigated. We show that the transmission characteristics of the grating are similar to those of an MMF subject to periodic microbending. Strong mode couplings take place in the grating when the pitch of the grating is equal to a specific value (∼1 mm), known as the critical spatial period of the fiber. The responses of some fabricated gratings to the axial strain and the change in the surrounding refractive index are measured and good sensitivities are achieved. Such MMF LPGs can be used potentially as physical and chemical sensors.